Electromagnetic beam steering antenna

ABSTRACT

Described embodiments include an electromagnetic beam steering apparatus. The apparatus includes a first blazed transmission diffraction grating component configured to angularly deflect an electromagnetic beam at a first blaze angle. The apparatus includes a second blazed transmission diffraction grating component configured to angularly deflect an electromagnetic beam at a second blaze angle. The apparatus includes an electromagnetic beam steering structure configured to independently rotate the first blazed transmission diffraction grating component and the second blazed transmission diffraction grating component about a coaxial axis such that an electromagnetic beam incident on the first blazed transmission diffraction grating component exits the second blazed transmission diffraction grating component as a steered electromagnetic beam.

If an Application Data Sheet (ADS) has been filed on the filing date ofthis application, it is incorporated by reference herein. Anyapplications claimed on the ADS for priority under 35 U.S.C. §§119, 120,121, or 365(c), and any and all parent, grandparent, great-grandparent,etc. applications of such applications, are also incorporated byreference, including any priority claims made in those applications andany material incorporated by reference, to the extent such subjectmatter is not inconsistent herewith.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of the earliest availableeffective filing date(s) from the following listed application(s) (the“Priority Applications”), if any, listed below (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC §119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Priority Application(s)).

PRIORITY APPLICATIONS

The present application constitutes a continuation of U.S. patentapplication Ser. No. 14/803,289, entitled ELECTROMAGNETIC BEAM STEERINGANTENNA, naming TOM DRISCOLL, RODERICK A. HYDE, MURIEL Y. ISHIKAWA,JORDIN T. KARE, NATHAN P. MYHRVOLD, TONY S. PAN, CLARENCE T. TEGREENE,YAROSLAV A. URZHUMOV, LOWELL L. WOOD, JR., VICTORIA Y. H. WOOD asinventors, filed 20, Jul. 2015, which is currently co-pending or is anapplication of which a currently co-pending application is entitled tothe benefit of the filing date.

If the listings of applications provided above are inconsistent with thelistings provided via an ADS, it is the intent of the Applicant to claimpriority to each application that appears in the DomesticBenefit/National Stage Information section of the ADS and to eachapplication that appears in the Priority Applications section of thisapplication.

All subject matter of the Priority Applications and of any and allapplications related to the Priority Applications by priority claims(directly or indirectly), including any priority claims made and subjectmatter incorporated by reference therein as of the filing date of theinstant application, is incorporated herein by reference to the extentsuch subject matter is not inconsistent herewith.

SUMMARY

For example, and without limitation, an embodiment of the subject matterdescribed herein includes an electromagnetic beam steering apparatus.The electromagnetic beam steering apparatus includes a first blazedtransmission diffraction grating component configured to angularlydeflect an electromagnetic beam at a first blaze angle. Theelectromagnetic beam steering apparatus includes a second blazedtransmission diffraction grating component configured to angularlydeflect an electromagnetic beam at a second blaze angle. Theelectromagnetic beam steering apparatus includes an electromagnetic beamsteering structure configured to independently rotate the first blazedtransmission diffraction grating component and the second blazedtransmission diffraction grating component about a coaxial axis suchthat an electromagnetic beam incident on the first blazed transmissiondiffraction grating component exits the second blazed transmissiondiffraction grating component as a steered electromagnetic beam.

In an embodiment, the apparatus includes a beam controller configured tocalculate a rotational position of the first blazed transmissiondiffraction grating component about the coaxial axis and a rotationalposition of the second blazed transmission diffraction grating componentpointing the steered electromagnetic beam at a selected target. In anembodiment, the apparatus includes an electromagnetic beam generatorconfigured to transmit the electromagnetic beam.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a method. The method includes rotating thefirst blazed transmission diffraction grating component around thecoaxial axis to a first selected position, and rotating the secondblazed transmission diffraction grating component around the coaxialaxis to a second selected position. The steered electromagnetic beam hasan azimuth angle θ and a zenith angle φ between zero and a finite anglefrom the coaxial axis. The azimuth angle θ and the zenith angle φ areresponsive to the first blaze angle, the second blaze angle, the firstselected position, and the second selected position.

In an embodiment, the method includes receiving information indicativeof a position of a target in a three dimensional space, and determiningthe first selected position and the second selected position pointingthe steered electromagnetic beam at the target. In an embodiment, themethod includes initiating the electromagnetic beam incident on thefirst blazed transmission diffraction grating component.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes an electromagnetic beam steering apparatus.The apparatus includes a first blazed transmission diffraction gratingcomponent having a first volumetric distribution of dielectric constantsconfigured to angularly deflect an electromagnetic beam at a first blazeangle. The apparatus includes a second blazed transmission diffractiongrating component having a second volumetric distribution of dielectricconstants configured to angularly deflect the electromagnetic beam at asecond blaze angle. The apparatus includes an electromagnetic beamsteering structure configured to independently rotate the first blazedtransmission diffraction grating component and the second blazedtransmission diffraction grating component about a coaxial axis suchthat an electromagnetic beam incident on the first blazed transmissiondiffraction grating component exits the second blazed transmissiondiffraction grating component as a steered electromagnetic beam.

In an embodiment, the apparatus includes a beam controller configured tocalculate a rotational position of the first blazed transmissiondiffraction grating component about the coaxial axis and a rotationalposition of the second blazed transmission diffraction grating componentabout the coaxial axis pointing the steered electromagnetic beam at aselected target. In an embodiment, the apparatus includes anelectromagnetic beam generator configured to transmit theelectromagnetic beam.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a method. The method includes passing anelectromagnetic beam through a first blazed transmission diffractiongrating component having a first volumetric distribution of dielectricconstants configured to angularly deflect the electromagnetic beam at afirst blaze angle relative to a coaxial axis and generating a firstoutput electromagnetic beam. The method includes passing the firstoutput electromagnetic beam through a second blazed transmissiondiffraction grating component having a second volumetric distribution ofdielectric constants configured to angularly deflect the first outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis and generating a steered electromagnetic beam. The steeredelectromagnetic beam having a direction relative to the coaxial axisthat is a vector sum of the first blaze angle and the second blazeangle.

In an embodiment, the method includes rotating the first blazedtransmission diffraction grating component around the coaxial axis to afirst selected position, and rotating the second blazed transmissiondiffraction grating component around the coaxial axis to a secondselected position. The steered electromagnetic beam has an azimuth angleθ and a zenith angle φ between zero and a finite angle from the coaxialaxis. The azimuth angle θ and the zenith angle φ are responsive to thefirst blaze angle, the second blaze angle, the first selected position,and the second selected position. In an embodiment, the method includesreceiving information indicative of a position of a target, anddetermining the first selected position and the second selected positionpointing the steered electromagnetic beam at the target. In anembodiment, the method includes initiating the electromagnetic beamincident on the first blazed transmission diffraction grating component.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a dual-channel electromagnetic beam steeringapparatus. The apparatus includes a first dual-channel blazedtransmission diffraction grating component having a first volumetricdistribution of dielectric constants configured to deflect at a firstblaze angle (i) a first electromagnetic beam having a first frequencyand (ii) a second electromagnetic beam having a second frequency. Theapparatus includes a second dual-channel blazed transmission diffractiongrating component having a second volumetric distribution of dielectricconstants configured to deflect at a second blaze angle (i) the firstelectromagnetic beam and (ii) the second electromagnetic beam. Theapparatus includes electromagnetic beam steering structure configured toindependently rotate the first dual-channel blazed transmissiondiffraction grating component and second dual-channel blazedtransmission diffraction grating component about a coaxial axis suchthat the first electromagnetic beam or second electromagnetic beamincident on the first dual-channel blazed transmission diffractiongrating component exit the second dual-channel blazed transmissiondiffraction grating component as a steered first electromagnetic beam ora steered second electromagnetic beam.

In an embodiment, the apparatus includes a beam controller configured tocalculate a rotational position of the first dual-channel blazedtransmission diffraction grating component about the coaxial axis and arotational position of the second dual-channel blazed transmissiondiffraction grating component pointing the steered electromagnetic beamat a selected target. In an embodiment, the apparatus includes anelectromagnetic beam generator configured to transmit theelectromagnetic beam.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a method. The method includes passing a firstincident electromagnetic beam having a first frequency or a secondincident electromagnetic beam having a second frequency through a firstdual-channel blazed transmission diffraction grating component having afirst volumetric distribution of dielectric constants deflecting thefirst incident electromagnetic beam or the second incidentelectromagnetic beam at a first blaze angle relative to a coaxial axis,and generating a first output electromagnetic beam having the firstfrequency or a second output electromagnetic beam having the secondfrequency. The method includes passing the first output electromagneticbeam or the second output electromagnetic beam through a seconddual-channel blazed transmission diffraction grating component having asecond volumetric distribution of dielectric constants deflecting thefirst output electromagnetic beam or the second output electromagneticbeam at a second blaze angle relative to the coaxial axis, andgenerating a first steered electromagnetic beam having the firstfrequency or a second steered electromagnetic beam having the secondfrequency. The first steered electromagnetic beam and the second steeredelectromagnetic beam both having a direction relative to the coaxialaxis that is a vector sum of the first blaze angle and the second blazeangle.

In an embodiment, the method includes rotating the first dual-channelblazed transmission diffraction grating component around the coaxialaxis to a first selected position, and rotating the second dual-channelblazed transmission diffraction grating component around the coaxialaxis to a second selected position. The first steered electromagneticbeam and the second steered electromagnetic beam each have an azimuthangle θ and a zenith angle φ between zero and a finite angle from thecoaxial axis. The azimuth angle θ and the zenith angle φ are responsiveto the first blaze angle, the second blaze angle, the first selectedposition, and the second selected position.

In an embodiment, the method includes receiving information indicativeof a position of a target in a three dimensional space, and determiningthe first selected position and the second selected position pointingthe steered electromagnetic beam at the target. In an embodiment, themethod includes initiating the first electromagnetic beam or the secondelectromagnetic beam incident on the first dual-channel blazedtransmission diffraction grating component.

The foregoing summary is illustrative only and is not intended to be inany way limiting. In addition to the illustrative aspects, embodiments,and features described above, further aspects, embodiments, and featureswill become apparent by reference to the drawings and the followingdetailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example first planar refractive component and asecond planar refractive component;

FIG. 2 illustrates an example electromagnetic beam steering apparatus;

FIG. 3 illustrates an example operational flow;

FIG. 4 illustrates an example electromagnetic beam steering apparatus;

FIG. 5 illustrates an example operational flow;

FIG. 6 illustrates an example electromagnetic beam steering apparatus;

FIG. 7 illustrates an example operational flow;

FIG. 8 illustrates an example electromagnetic beam steering apparatus;

FIG. 9 illustrates an example operational flow;

FIG. 10 illustrates an example dual-channel electromagnetic beamsteering apparatus;

FIG. 11 illustrates modeling results for a dual-channel blazedtransmission diffraction grating component having a volumetricdistribution of dielectric constants;

FIG. 12A illustrates a deflection of the first electromagnetic beam atfrequency f0 at a selected blaze angle;

FIG. 12B illustrates a deflection of the second electromagnetic beam atfrequency f1 at the selected blaze angle of FIG. 12A;

FIG. 13 illustrates an example operational flow;

FIG. 14 illustrates an example electromagnetic beam steering apparatus;

FIG. 15 illustrates an example operational flow;

FIG. 16 illustrates an electromagnetic beam steering apparatus; and

FIG. 17 illustrates an example operational flow.

DETAILED DESCRIPTION

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/257,175, entitled SUB-NYQUISTHOLOGRAPHIC APERTURE ANTENNA CONFIGURED TO DEFINE SELECTABLE, ARBITRARYCOMPLEX ELECTROMAGNETIC FIELDS, naming Pai-Yen Chen et al. as inventors,filed on Apr. 21, 2014. That application is incorporated by referenceherein, including any subject matter included by reference in thatapplication.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/257,187, entitled SUB-NYQUISTHOLOGRAPHIC APERTURE ANTENNA CONFIGURED TO DEFINE SELECTABLE, ARBITRARYCOMPLEX ELECTROMAGNETIC FIELDS, naming Pai-Yen Chen et al. as inventors,filed on Apr. 21, 2014. That application is incorporated by referenceherein, including any subject matter included by reference in thatapplication.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/257,386, entitled SYSTEM WIRELESSLYTRANSFERRING POWER TO A TARGET DEVICE OVER A TESTED TRANSMISSIONPATHWAY, naming Pai-Yen Chen et al. as inventors, filed on Apr. 21,2014. That application is incorporated by reference herein, includingany subject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/257,415, entitled SYSTEM WIRELESSLYTRANSFERRING POWER TO A TARGET DEVICE OVER A MODELED TRANSMISSIONPATHWAY WITHOUT EXCEEDING A RADIATION LIMIT FOR HUMAN BEINGS, namingPai-Yen Chen et al. as inventors, filed on Apr. 21, 2014. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,740, now U.S. Pat. No.8,168,930, entitled BEAM POWER FOR LOCAL RECEIVERS, naming Roderick A.Hyde et al. as inventors, filed on Sep. 30, 2008. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,737, now U.S. Pat. No.8,058,609, entitled BEAM POWER WITH MULTIPOINT BROADCAST, namingRoderick A. Hyde et al. as inventors, filed on Sep. 30, 2008. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,755, now U.S. Pat. No.8,803,053, entitled BEAM POWER WITH MULTIPOINT RECEPTION, namingRoderick A. Hyde et al. as inventors, filed on Sep. 30, 2008. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,741, now U.S. Pat. No.7,786,419, entitled BEAM POWER WITH BEAM REDIRECTION, naming Roderick A.Hyde et al. as inventors, filed on Sep. 30, 2008. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. Patent Application No. 61/455,171, entitled SURFACE SCATTERINGANTENNAS, naming Nathan Kundtz as inventor, filed Oct. 15, 2010. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 13/317,338, entitled SURFACE SCATTERINGANTENNAS, naming Adam Bily et al. as inventors, filed Oct. 14, 2011.That application is incorporated by reference herein, including anysubject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 13/838,934, entitled SURFACE SCATTERINGANTENNA IMPROVEMENTS, naming Adam Bily et al. as inventors, filed Mar.15, 2013. That application is incorporated by reference herein,including any subject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/102,253, entitled SURFACE SCATTERINGREFLECTOR ANTENNA, naming Jeffrey A. Bowers et al. as inventors, filedDec. 10, 2013. That application is incorporated by reference herein,including any subject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/226,213, entitled SURFACE SCATTERINGANTENNA ARRAY, naming Jeffrey A. Bowers et al. as inventors, filed Mar.26, 2014, is related to the present application. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/334,368, entitled ARTIFICIALLYSTRUCTURED B₁ MAGNETIC FIELD GENERATOR FOR MRI AND NMR DEVICES, namingTom Driscoll et al. as inventors, filed Jul. 17, 2014. That applicationis incorporated by reference herein, including any subject matterincluded by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/334,398, entitled ARTIFICIALLYSTRUCTURED UNIT CELLS PROVIDING LOCALIZED B₁ MAGNETIC FIELDS FOR MRI ANDNMR DEVICES, naming Tom Driscoll et al. as inventors, filed Jul. 17,2014. That application is incorporated by reference herein, includingany subject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/334,424, entitled ELECTRONICALLYCONTROLLABLE GROUPS OF ARTIFICIALLY STRUCTURED UNIT CELLS PROVIDINGLOCALIZED B₁ MAGNETIC FIELDS FOR MRI AND NMR DEVICES, naming TomDriscoll et al. as inventors, filed Jul. 17, 2014. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/334,450, entitled CANCELLATION OF ANELECTRIC FIELD COMPONENT OF A MAGNETIC FIELD GENERATED BY ARTIFICIALLYSTRUCTURED ELECTROMAGNETIC UNIT CELLS, naming Tom Driscoll et al. asinventors, filed Jul. 17, 2014. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/619,393, entitled MINIMALLY-INVASIVETISSUE ABLATION USING HIGH CONTRAST ELECTRONIC FIELDS, naming YaroslavUrzhumov as inventor, filed Feb. 11, 2015. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/689,871, entitled METHODS AND SYSTEMFOR PERFORMING MAGNETIC INDUCTION TOMOGRAPHY, naming Tom Driscoll et al.as inventors, filed Apr. 17, 2015. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/619,456, entitled ELECTROMAGNETICFIELD PERTURBING OBJECT HAVING A BIOCOMPATIBLE EXTERIOR SURFACE AND ASELECTED DIELECTRIC PERMITTIVITY VALUE OR A SELECTED MAGNETICPERMEABILITY VALUE, naming Yaroslav Urzhumov as inventor, filed Feb. 11,2015. That application is incorporated by reference herein, includingany subject matter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/638,961, entitled HOLOGRAPHIC MODECONVERSION FOR ELECTROMAGNETIC RADIATION, naming Tom Driscoll et al. asinventors, filed Mar. 4, 2015. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/708,043, entitled HOLOGRAPHIC MODECONVERSION FOR TRANSMISSION LINES, naming Tom Driscoll et al. asinventors, filed May 8, 2015. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/058,855, entitled ANTENNA SYSTEMFACILITATING REDUCTION OF INTERFERING SIGNALS, naming Roderick A. Hydeet al. as inventors, filed Oct. 21, 2013. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/059,188, entitled ANTENNA SYSTEMHAVING AT LEAST TWO APERTURES FACILITATING REDUCTION OF INTERFERINGSIGNALS, naming Roderick A. Hyde et al. as inventors, filed Oct. 21,2013. That application is incorporated by reference herein, includingany subject matter included by reference in that application.

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here.

FIG. 1 illustrates an example first planar refractive component 110 anda second planar refractive component 120. The first planar refractivecomponent includes a first tangential refractive index gradient 112deflecting an electromagnetic beam at a first deflection angle 134relative to an axis 106 normal (e.g. Z-axis 102) to a major surface 114of the first planar refractive component. The electromagnetic beam isillustrated as an electromagnetic beam 130.1. The transmitted orrefracted electromagnetic beam is illustrated by electromagnetic beam132. In an embodiment, the first tangential refractive index gradientproduces a gradual phase shift accumulation up to a across the majorsurface of the planar refractive component. In an embodiment, the phaseshift is a function of a linear position along the major surface of therefractive component. In an embodiment, the electromagnetic beamincludes a finite-width electromagnetic beam. In an embodiment, theelectromagnetic beam includes a plane wave electromagnetic beam. In anembodiment, the first deflection angle is a function of phase gradientsintroduced by the first tangential refractive index gradient of thefirst planar refractive component. In an embodiment, the first planarcomponent may have a cylindrical shape, a parallelepiped shape, or othershape with substantially parallel major surfaces in the XY plane of axis102.

The second planar refractive component 120 includes a second tangentialrefractive index gradient 122 deflecting an electromagnetic beam at asecond deflection angle 138 relative to an axis 107 normal (e.g. Z-axis102) to a major surface 124 of the second planar refractive component.The electromagnetic beam is illustrated as an electromagnetic beam130.2. The transmitted or refracted electromagnetic beam is illustratedby electromagnetic beam 136. In an embodiment, the second planarcomponent may have a cylindrical shape, a parallelepiped shape, or othershape with substantially parallel major surfaces in the XY plane of axis102.

FIG. 2 illustrates an example electromagnetic beam steering apparatus200 and a reference three-dimensional axis 102. The electromagnetic beamsteering apparatus includes the first planar refractive component 110and the second planar refractive component 120. The electromagnetic beamsteering apparatus includes an electromagnetic beam steering structure250 configured to independently rotate 139 the first planar refractivecomponent and the second planar refractive component about a coaxialaxis 205 such that an electromagnetic beam 130 incident on the firstplanar refractive component exits the second planar refractive componentas a steered electromagnetic beam 236. In an embodiment, theelectromagnetic beam steering apparatus may steer an electromagneticbeam in a transmit mode or in a receive mode. For example, in anembodiment, the electromagnetic beam steering structure may function oroperate in a Risley prism beam steering manner.

In an embodiment, the electromagnetic beam 130 includes a radiofrequencyelectromagnetic beam. For example, the radiofrequency electromagneticbeam may include a microwave band radiofrequency electromagnetic beam.For example, a radiofrequency electromagnetic beam may include a 1 GHzto 300 GHz radiofrequency electromagnetic beam. For example, theradiofrequency electromagnetic beam may include a radiofrequencyelectromagnetic beam with a free space wavelength between 30 cm to 1 mm.In an embodiment, the electromagnetic beam includes a light wavelengthelectromagnetic beam. For example, a light wavelength electromagneticbeam may include an infrared or a visible light wavelengthelectromagnetic beam.

In an embodiment, the first planar refractive component 110 includes twoopposed generally planar and parallel major surfaces and a thickness 116that is less than the free-space wavelength of the electromagnetic beam.In an embodiment, a planar surface of the two opposed generally planarand parallel major surfaces has a radius of curvature that is largerelative to the thickness. In an embodiment, the radius of curvature isgreater than ten times the thickness. In an embodiment, the radius ofcurvature includes a cylindrical radius of curvature. In an embodiment,a major surface 114 of the first planar refractive component includes agenerally or substantially flat major surface. In an embodiment, areceiving or transmitting surface of the first planar refractivecomponent includes an arbitrary surface approximating a flat surface.

In an embodiment, the first tangential refractive index gradient 112 ofthe first planar refractive component 110 includes a refractive indexgradient coplanar with the first planar refractive component. In anembodiment, the first planar refractive component has a planar surfacediameter greater than the free-space wavelength of the electromagneticbeam. In an embodiment, the first planar refractive component has aplanar surface diameter much greater than the free-space wavelength ofthe electromagnetic beam.

In an embodiment, the first planar refractive component 110 and thesecond planar refractive component 120 each have a thickness 116 and 126respectively that is less than the free-space wavelength of the incidentelectromagnetic beam 130 (hereafter free-space subwavelength thickness).In an embodiment, the free-space subwavelength thickness includes asubwavelength thickness of less than one-half of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-fifth of the free-space wavelength of the electromagnetic beam. Inan embodiment, the free-space subwavelength thickness includes asubwavelength thickness of less than one-tenth of the free-spacewavelength of the electromagnetic beam.

In an embodiment, the first planar refractive component 110 includes afirst planar refractive component with a substantially uniformtransmissivity. For example, uniformly transmissivity may include anapproximately constant transmissivity independent of a position on theplanar surface. In an embodiment, the first planar refractive componenthas a tangential refractive index gradient deflecting a normal incidentelectromagnetic beam 130 or 130.1 at a first deflection angle 134. In anembodiment, the first tangential refractive index gradient 112 of thefirst planar refractive component creates a linearly varying propagationdelay. In an embodiment, the first planar refractive component includesa tangential refractive index gradient and a selectable electromagneticbeam impedance profile deflecting an incident electromagnetic beam 130or 130.1 at a first deflection angle 134. For example, beam impedancecontrols reflectance, so as the refractive index increases, reflectivitygoes up unless the beam impedance is adjusted to compensate. In anembodiment, the first planar refractive component includes anon-reflective first planar refractive component. For example, anon-reflective first planar refractive component may be implemented byimpedance matching.

In an embodiment, the first planar refractive component 110 includes anartificially structured effective media. In an embodiment, anartificially structured effective media may include a composite materialhaving at the constituent level varying and inhomogeneous materials,each having their own individual microscopic properties, and at thecomposite level effectively described by macroscopic properties. Thus,that composite material may be described as effective media. As usedherein effective media may include the singular or plural. In anembodiment, the artificially structured effective media includes acomposite material. In an embodiment, the artificially structuredeffective media includes an artificially structured subwavelengtheffective media. In an embodiment, the artificially structured effectivemedia includes low-loss dielectrics. In an embodiment, the artificiallystructured effective media includes all-dielectric metamaterials. In anembodiment, the artificially structured effective media includesnegative permittivity or negative permeability constituent materials. Inan embodiment, the artificially structured effective media includesartificially structured subwavelength electromagnetic unit cells. Forexample, the artificially structured subwavelength electromagnetic unitcells may include at least three subwavelength electromagnetic unitcells having a varying spacing, permittivity, or permeability. In anembodiment, the artificially structured effective media includesartificially structured subwavelength metamaterial unit cells. In anembodiment, the artificially structured effective media includes anartificially structured meta-surface or meta-interface. For example, anartificially structured meta-surface or meta-interface may include asubwavelength unit cell structure. For example, an artificiallystructured meta-interface may include a concentrated negativepermittivity or permeability in a thin interface. In an embodiment, theartificially structured effective media includes at least twosubwavelength components having different electromagnetic beamdispersion characteristics. In an embodiment, the first planarrefractive component 110 includes a first planar scattering componenthaving the first tangential refractive index gradient 112.

In an embodiment, the first planar refractive component 110 includes afirst composite structure having a first refractive subcomponent havinga first tangential refractive index gradient deflecting anelectromagnetic beam at a first sub-deflection angle (first deflectedincident electromagnetic beam) and a second refractive subcomponenthaving a second tangential refractive index gradient deflecting thefirst deflected incident electromagnetic beam at a second sub-deflectionangle. The first refractive subcomponent and the second refractivesubcomponent are arranged in the first planar refractive component suchthat the electromagnetic beam passes through them in series. In anembodiment, the second planar refractive component 120 includes a secondcomposite structure. The second composite structure includes a thirdtangential refractive index gradient deflecting a second electromagneticbeam incident on the second composite structure at a thirdsub-deflection angle (third deflected incident electromagnetic beam) anda fourth refractive subcomponent having a fourth tangential refractiveindex gradient deflecting the third deflected incident electromagneticbeam at a fourth sub-deflection angle. The third refractive subcomponentand the fourth refractive subcomponent are arranged in the second planarrefractive component such that the electromagnetic beam passes throughthem in series.

In an embodiment, the first planar refractive component 110 includes afirst achromatic planar refractive component having a first tangentialrefractive index gradient 112 deflecting an electromagnetic beam 130 or130.1 at a first deflection angle 134 over a finite range ofwavelengths. For example, a finite range of wavelengths includes adiscrete set of wavelengths. An embodiment of an achromatic planarrefractive component having a tangential refractive index gradient isdescribed in F. Aieta, et. al, Multiwavelength achromatic metasurfacesby dispersive phase compensation, Sciencexpress 1 (19 Feb. 2015)(10.1126/science.aaa2494). In an embodiment, the first achromatic planarrefractive component includes an artificially structured effective mediacreating an electromagnetic beam dispersion characteristic. In anembodiment, the artificially structured effective media includes aneffective negative permittivity or negative permeability media. In anembodiment, the artificially structured effective media includesartificially structured subwavelength electromagnetic unit cells. In anembodiment, the artificially structured effective media includesartificially structured subwavelength metamaterial unit cells. In anembodiment, the artificially structured effective media includesartificially structured meta-surface. For example, an artificiallystructured meta-surface includes a subwavelength structure. In anembodiment, the achromatic planar refractive component includes anegatively dispersive refractive index as a function of frequency(dn/df<0). In an embodiment, the achromatic planar refractive componentincludes an artificially structured effective media having a negativelysloped refractive index as a function of frequency (dn/df<0). In anembodiment, the achromatic planar refractive component includes a firstartificially structured effective media creating a first electromagneticbeam dispersion characteristic and a second artificially structuredeffective media creating a second electromagnetic beam dispersioncharacteristic. For example, the first artificially structured effectivemedia and the second artificially structured effective media may be indifferent layers of the achromatic planar refractive component. Forexample, the first artificially structured effective media and thesecond artificially structured effective media may be intermingled inthe achromatic planar refractive component.

In an embodiment, the first planar refractive component 110 and thesecond planar refractive component 120 each include an engineereddispersion compensation for an angular deflection variation as afunction of frequency producing an achromatic response over a finiterange of electromagnetic beam wavelengths. In an embodiment, theengineered dispersion compensation includes cancelling out thewavelength dependence of the diffraction phenomena. For example, theengineered dispersion compensation may include using a negatively slopedrefractive index.

In an embodiment, the first deflection angle 134 is substantially thesame as the second deflection angle 138. In an embodiment, the firstdeflection angle is within five degrees of the second deflection angle.In an embodiment, the first deflection angle is within 2.5 degrees ofthe second deflection angle. In an embodiment, the first planarrefractive component 110 includes a first planar blazed transmissiongrating component deflecting an electromagnetic beam 130 or 130.1 at afirst deflection angle 134. In an embodiment, the first deflection angleincludes a first deflection angle optimized for beam steering.

In an embodiment, the first tangential refractive index gradient 112includes a piecewise linear refractive index deflecting theelectromagnetic beam 130 or 130.1 at the first deflection angle 134. Inan embodiment, the first planar refractive component 110 and the secondplanar refractive component 120 each respectively include a substratetransparent to the electromagnetic beam. In an embodiment, the substrateincludes a substrate nominally transparent to the electromagnetic beam.

In an embodiment, the first planar refractive component 110 includes anartificially structured effective media having anelectronically-selectable tangential refractive index gradient 112deflecting the electromagnetic beam 130 or 130.1 at a first selectabledeflection angle 134 if in a first selected state and a deflecting theelectromagnetic beam at a second selectable deflection angle if in asecond selected state. For example, the first selected state may be an“off-state” and the second selected state may be an “on-state.” In analternative embodiment, the artificially structured effective media mayinclude a composite structure having a first refractive subcomponenthaving a first tangential refractive index gradient deflecting theincident electromagnetic beam at a first deflection angle and a secondrefractive subcomponent having the electronically selectable refractivegradient.

In an embodiment, the major surface 114 of the first planar refractivecomponent 110 includes at least two layers of voxels of artificiallystructured effective media. Each voxel of the artificially structuredeffective media having electronically-selectable tangential refractiveindex gradient deflecting an electromagnetic beam 130 or 130.1 at afirst selected deflection angle if in a first selected state and adeflecting the electromagnetic beam at a second selected deflectionangle if in a second selected state. For example, in an embodiment, thevoxels of artificially structured effective media may include unitcells. For example, in an embodiment, the voxels of artificiallystructured effective media may be arranged in a three-dimensionalassembly. For example, in an embodiment each voxel or unit cell has oneof two fixed refractive index values, where one value is that of freespace and the other value is the range of n=1.3-3. For example, in anembodiment, each voxel or unit cell could use one of two differentrefractive index values other than free space where a cell that is “off”has the reflective index value of free space. For example, in anembodiment, a major surface 114 of the first planar refractive component110 includes at least three layers of voxels of artificially structuredeffective media providing a tunable phase gradient.

In an embodiment, the electromagnetic beam steering structure 250includes an electronically controlled electromagnetic beam steeringstructure. In an embodiment, the electromagnetic beam steering structureis configured to independently and physically rotate or counter rotatethe first planar refractive component and the second planar refractivecomponent about the coaxial axis 205. In an embodiment, the coaxial axisis normal to the major surface 114 of the first planar refractivecomponent 110 and the major surface 124 of the second planar refractivecomponent 120. In an embodiment, the electromagnetic beam steeringstructure is configured to rotate the first planar refractive componentand the second planar refractive component about the coaxial axis whilemaintaining an electromagnetic beam path alignment through the firstplanar refractive component and the second planar refractive component.In an embodiment, the electromagnetic beam steering structure isconfigured to rotate the first planar refractive component using an edgedrive mechanism. For example, an edge drive mechanism may include a beltdrive or a roller drive. For example, an edge drive mechanism mayinclude separate motors for each component. In an embodiment, theelectromagnetic beam steering structure is configured to rotate thefirst planar refractive component using an integral edge drive motor oran integral on-axis motor. For example, an integral edge drive mayinclude magnetic coils coupled to a magnetic-material track on the firstplanar refractive component, or an inchworm mechanism. In an embodiment,the electromagnetic beam steering structure is configured tomechanically rotate the first planar refractive component using theintegral edge drive motor. In an embodiment, the electromagnetic beamsteering structure is configured to rotate the first planar refractivecomponent and the second planar refractive component about the coaxialaxis independently of each other. In an embodiment, the coaxial axisincludes a coaxial axis rotationally symmetric and coaxial to each ofthe planar refractive components 110 and 120.

In an embodiment, the electromagnetic beam 130 includes a circularlypolarized electromagnetic beam. In an embodiment, the first planarrefractive component 110 and the second planar refractive component 120each include a polarization-independent refractive index gradients 112and 122.

In an embodiment, the apparatus 200 further includes a firstquarter-wave plate positioned in an electromagnetic beam path betweenthe first planar refractive component 110 and a source of the incidentelectromagnetic beam 130. In an embodiment, the apparatus includes asecond quarter-wave plate positioned in an exit electromagnetic beampath downstream of the second planar refractive component 120. In thisembodiment, the first quarter-wave plate converts linearly-polarizedinput electromagnetic beam into circularly-polarized radiation forsteering, and the second quarter-wave plate converts the electromagneticbeam back to linearly-polarized if needed. In an embodiment, thequarter-wave plates may be integrated with antireflection layers on theplanar refractive components.

In an embodiment, the first planar refractive component 110 and thesecond planar refractive component 120 are each arranged in theelectromagnetic beam steering structure 250 with their beam receivingfaces parallel to each other and normal to the coaxial axis 205.

In an embodiment, the steered electromagnetic beam 236 has directionthat is a vector sum of the first deflection angle 134 of the firstplanar refractive component 110 and the second deflection angle 238 ofthe second planar refractive component 120. In an embodiment, theelectromagnetic beam 130 incident on the first planar refractivecomponent exits the second planar refractive component as a steeredelectromagnetic beam 236 having a direction (azimuth angle θ 139 andzenith angle φ 238) that is a vector sum of the first deflection angleof the first planar refractive component and the second deflection angleof the second planar refractive component. In an embodiment, the steeredelectromagnetic beam has a controllable tilt at an angle φ relative tothe coaxial axis 205. In an embodiment, the steered electromagnetic beamhas a controllable rotation at an azimuth angle θ about the coaxial axis205. In an embodiment, the electromagnetic beam steering structure isconfigured to steer the electromagnetic beam 130 propagating along thecoaxial axis normal to the first planar refractive component and thesecond planar refractive component to an azimuth angle θ and a zenithangle φ between zero and a finite angle from the coaxial axis. In anembodiment, the electromagnetic beam steering structure is configured tosteer the transmitted deflected electromagnetic beam to a selectableportion of a field of regard. In an embodiment, the electromagnetic beamsteering structure is configured to steer the transmittedelectromagnetic beam within a continuous range of directions within afield of regard.

In an embodiment, the apparatus 200 includes a beam controller 280configured to calculate a rotational position of the first planarrefractive component 110 about the coaxial axis 205 and a rotationalposition of the second planar refractive component 120 about the coaxialaxis pointing the steered electromagnetic beam 236 at a selected target295. In an embodiment, the beam controlled may be configured to acquire,track, and point at the selected target.

In an embodiment, the apparatus 200 includes an electromagnetic beamgenerator 286 configured to transmit the electromagnetic beam to thefirst planar refractive component 110. In an embodiment, theelectromagnetic beam generator includes a radio frequency antenna. In anembodiment, the radio frequency antenna includes a microwave antenna. Inan embodiment, the radio frequency antenna includes parabolic reflector,horn with dielectric lens, or slotted waveguide. In an embodiment, theradio frequency antenna includes a slotted waveguide. In an embodiment,the radio frequency antenna includes a holographic planar metamaterialantenna. In an embodiment, the radio frequency antenna includes a hornwith a dielectric lens. In an embodiment, the radio frequency antennaincludes a patch antenna. In an embodiment, the electromagnetic beamgenerator includes an optical radiation transmitter. In an embodiment,the electromagnetic beam generator includes an optical radiationreceiver. In an embodiment, the electromagnetic beam generator includesan optical radiation transceiver. In an embodiment, the electromagneticbeam generator includes a laser waveguide configured to direct anoptical electromagnetic beam at the first planar refractive component.

Various embodiments or variations of the first planar refractivecomponent 110 are described herein. In an embodiment, the second planarrefractive component 120 may include one or more of the embodiments orvariations described for the first planar refractive component.

FIG. 3 illustrates an example operational flow 300. After a startoperation, the operational flow includes a first deflecting operation310. The first deflecting operation includes passing an electromagneticbeam through a first planar refractive component having a firsttangential refractive index gradient, deflecting the electromagneticbeam at a first deflection angle relative to a coaxial axis, andgenerating a first output electromagnetic beam. In an embodiment, thefirst deflecting operation may be implemented by the electromagneticbeam 130.1 passing through the first planar refractive component 110,being deflected at the first deflection angle 134 relative to thecoaxial axis 106, and generating the first output electromagnetic beam,illustrated as the electromagnetic beam 132, as described in conjunctionwith FIG. 1. In an embodiment, the first deflecting operation may beimplemented by the electromagnetic beam 130 passing through the firstplanar refractive component 110, being deflected at the first deflectionangle 134 relative to the coaxial axis 205, and generating the firstoutput electromagnetic beam, illustrated as the electromagnetic beam232, as described in conjunction with FIG. 2.

A second deflecting operation 320 includes passing the first outputelectromagnetic beam through a second planar refractive component havinga second tangential refractive index gradient, deflecting the firstoutput electromagnetic beam at a second deflection angle relative to thecoaxial axis, and generating a steered electromagnetic beam. In anembodiment, the second deflecting operation may be implemented by thefirst output electromagnetic beam, illustrated as the electromagneticbeam 130.2, passing through the second planar refractive component 120,being deflected at the second deflection angle 138 relative to thecoaxial axis 107, and generating a steered electromagnetic beam,illustrated as the electromagnetic beam 136, as described in conjunctionwith FIG. 1. In an embodiment, the second deflecting operation may beimplemented by the first output electromagnetic beam, illustrated as theelectromagnetic beam 232 passing through the second planar refractivecomponent 120, being deflected at the second deflection angle 238relative to the coaxial axis 205, and generating a steeredelectromagnetic beam, illustrated as the steered electromagnetic beam236, as described in conjunction with FIG. 2. The steeredelectromagnetic beam having a direction relative to the coaxial axisthat is a vector sum of the first deflection angle 134 and the seconddeflection angle 238. The operational flow includes an end operation. Inan embodiment, the first planar refractive component includes anartificially structured effective media.

In an embodiment, the operational flow 300 includes rotating the firstplanar refractive component around the coaxial axis to a first selectedposition, and rotating the second planar refractive component around thecoaxial axis to a second selected position. In an embodiment, thesteered electromagnetic beam 238 has an azimuth angle θ 139. The azimuthangle describes a rotation about the coaxial axis 205. The steeredelectromagnetic beam 238 has a zenith angle φ 238. The zenith angledescribes a deflection from the coaxial axis between zero and finiteangle from the coaxial axis. The azimuth angle θ and the zenith angle φare responsive to the first deflection angle, the second deflectionangle, the first selected position, and the second selected position.

In an embodiment, the operational flow 300 includes a targetingoperation. The targeting operation includes receiving informationindicative of a position of a target 295, and determining the firstselected position and the second selected position pointing the steeredelectromagnetic beam 230 at the target. In an embodiment, the targetingoperation may be implemented using the beam controller 280 described inconjunction with FIG. 2. In an embodiment, the receiving includesreceiving information indicative of a position of the target in a threedimensional space.

In an embodiment, the operational flow 300 includes initiating theelectromagnetic beam incident on the first planar refractive component.In an embodiment, the initiating may be implemented using the beamgenerator 286 described in conjunction with FIG. 2.

FIG. 4 illustrates an example electromagnetic beam steering apparatus400 and a reference three-dimensional axis 402. The apparatus includes afirst planar refractive component 410 having a first tangentialpiecewise linear refractive index 412 deflecting an electromagnetic beam430 at a first deflection angle 434 relative to an axis 405 normal (e.g.Z-axis 102) to a major surface 414 of the first planar refractivecomponent. In an embodiment, the first tangential piecewise linearrefractive index includes a continuously varying index of refraction. Inan embodiment, the first tangential piecewise linear refractive indexincludes a continuously spatially varying index of refraction. Forexample, the tangential piecewise linear refractive index may include anon-constant media providing a continuously varying index of refraction.The index is approximated or modeled using piece-piecewise-linearapproximations of the non-linear rays. In an embodiment, the firstplanar component may have a cylindrical shape, a parallelepiped shape,or other shape with substantially parallel major surfaces in the XYplane of axis 402. The apparatus includes a second planar refractivecomponent 420 having a second tangential piecewise linear refractiveindex 422 deflecting an electromagnetic beam 432 at a second deflectionangle 438 relative to an axis 405 normal (e.g. Z-axis 102) to a majorsurface 424 of the second planar refractive component. In an embodiment,the first deflection angle and the second deflection angle may besubstantially similar. The apparatus includes an electromagnetic beamsteering structure 450 configured to independently rotate 439 the firstplanar refractive component and second planar refractive component aboutthe coaxial axis 405 such that the electromagnetic beam 430 incident onthe first planar refractive component exits the second planar refractivecomponent as a steered electromagnetic beam, illustrated by the firstoutput electromagnetic beam 432. In an embodiment, the electromagneticbeam steering apparatus may steer an electromagnetic beam in a transmitmode or in a receive mode. For example, in an embodiment, theelectromagnetic beam steering structure may function or operate in aRisley prism beam steering manner.

In an embodiment, the electromagnetic beam 430 includes a radiofrequencyelectromagnetic beam. For example, a radiofrequency electromagnetic beammay include a microwave band radiofrequency electromagnetic beam. Forexample, a radiofrequency electromagnetic beam may include a 1 GHz to300 GHz radiofrequency electromagnetic beam. For example, aradiofrequency electromagnetic beam may include a radiofrequencyelectromagnetic beam with a free space wavelength between 30 cm to 1 mm.In an embodiment, the electromagnetic beam includes a light wavelengthelectromagnetic beam. For example, a light wavelength electromagneticbeam may include an infrared or a visible light wavelengthelectromagnetic beam.

In an embodiment, the first planar refractive component 410 includes twoopposed generally planar and parallel major surfaces and a thickness 416that is less than the free-space wavelength of the electromagnetic beam.In an embodiment, a planar surface of the two opposed generally planarand parallel major surfaces has a radius of curvature that is largerelative to the thickness. In an embodiment, the radius of curvature isgreater than ten times the thickness. In an embodiment, the radius ofcurvature includes a cylindrical radius of curvature. In an embodiment,a major surface 414 of the first planar refractive component includes agenerally or substantially flat major surface. In an embodiment, areceiving or transmitting surface of the first planar refractivecomponent includes an arbitrary surface approximating a flat surface.

In an embodiment, the first planar refractive component 410 and thesecond planar refractive component 420 each have a thickness (416, 426)less than the free-space wavelength of the incident electromagnetic beam(hereafter free-space subwavelength thickness). In an embodiment, thefree-space subwavelength thickness includes a subwavelength thickness ofless than one-half of the free-space wavelength of the electromagneticbeam. In an embodiment, the free-space subwavelength thickness includesa subwavelength thickness of less than one-fifth of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-tenth of the free-space wavelength of the electromagnetic beam. Inan embodiment, the piecewise linear refraction index includes apiecewise constant gradient.

In an embodiment, the first piecewise linear refraction index 412includes a piecewise continuous refraction gradient withdiscontinuities. In an embodiment, the first piecewise linear refractionindex includes a spacewise dependent index of refraction. In anembodiment, the first piecewise linear refraction index includes aperiodically repeating refraction index profile. In an embodiment, thefirst piecewise linear refraction index includes a linearly varyinggradient index transverse to the plane of the first planar refractivecomponent.

In an embodiment, the first planar refractive component 410 includes anartificially structured effective media configured to produce thepiecewise linear refractive index 412. In an embodiment, theartificially structured effective media includes a composite material.In an embodiment, the artificially structured effective media includesan effective negative permittivity or negative permeability media. In anembodiment, the artificially structured effective media includesartificially structured subwavelength electromagnetic unit cells. In anembodiment, the artificially structured effective media includesartificially structured subwavelength metamaterial unit cells. In anembodiment, the artificially structured effective media includesartificially structured metamaterial surface. In an embodiment, theartificially structured effective media includes artificially structuredmeta-surface or meta-interface. In an embodiment, the artificiallystructured meta-surface or meta-interface includes subwavelengthcomponents or elements.

In an embodiment, the first planar refractive component 410 includes anartificially structured effective media having electronically-selectablepiecewise linear refractive index 412 deflecting the electromagneticbeam 430 at a first selected deflection angle if in a first selectedstate and a deflecting the electromagnetic beam at a second selecteddeflection angle if in a second selected state. In an embodiment forexample, the first selected state may be an off-state, and the secondselected state may be an on-state.

In an embodiment, the major surface 414 of the first planar refractivecomponent 410 includes at least two layers of voxels of artificiallystructured effective media. Each voxel of the artificially structuredeffective media having electronically-selectable piecewise linearrefractive index gradient 412 deflecting the electromagnetic beam 430incident on the major surface 414 at a first deflection angle if in afirst selected state and deflecting the incident electromagnetic beam ata second deflection angle if in a second selected state. In anembodiment, the voxels of artificially structured effective media mayinclude subwavelength unit cells. In an embodiment, the voxels ofartificially structured effective media include a three-dimensionalassembly of artificially structured effective media. In an embodiment,each voxel or unit cell has one of two fixed refractive index values,where one value is that of free space and the other value is the rangeof n=1.3-3. In an embodiment, each voxel or unit cell has one of twodifferent refractive index values.

In an embodiment, the apparatus 400 includes a beam controller 480configured to calculate a rotational position of the first planarrefractive component 410 about the coaxial axis 405 and a rotationalposition of the second planar refractive component 420 about the coaxialaxis pointing the steered electromagnetic beam at the selected target295. In an embodiment, the beam controller may be configured to acquire,track, and point at the selected target. In an embodiment, the apparatusincludes an electromagnetic beam generator 486 configured to transmitthe electromagnetic beam.

Various embodiments or variations of the first planar refractivecomponent 410 are described herein. In an embodiment, the second planarrefractive component 420 may include one or more of the embodiments orvariations described for the first planar refractive component.

FIG. 5 illustrates an example operational flow 500. After a startoperation, the operational flow includes a first deflecting operation510. The first deflecting operation includes passing an electromagneticbeam through a first planar refractive component having a firsttangential piecewise linear refractive index, deflecting theelectromagnetic beam at a first deflection angle relative to a coaxialaxis, and generating a first output electromagnetic beam. In anembodiment, the first deflecting operation may be implemented by theelectromagnetic beam 430 passing through the first planar refractivecomponent 410 having the first tangential piecewise linear refractiveindex 412, deflecting the electromagnetic beam at the first deflectionangle 434 relative to the coaxial axis 405, and generating the firstoutput electromagnetic beam 432 as described in conjunction with FIG. 4.

A second deflecting operation 520 includes passing the first outputelectromagnetic beam through a second planar refractive component havinga second tangential piecewise linear refractive index, deflecting thefirst output electromagnetic beam at a second deflection angle relativeto the coaxial axis, and generating a steered electromagnetic beam. Inan embodiment, the second deflecting operation may be implemented bypassing the first output electromagnetic beam 432 through the secondplanar refractive component 420 having the second tangential piecewiselinear refractive index 422, deflecting the first output electromagneticbeam at the second deflection angle 438 relative to the coaxial axis405, and generating the steered electromagnetic beam 436 as described inconjunction with FIG. 4. The steered electromagnetic beam having adirection relative to the coaxial axis that is a vector sum of the firstdeflection angle and the second deflection angle. The operational flowincludes an end operation. In an embodiment, the first planar refractivecomponent includes an artificially structured effective media.

In an embodiment, the operational flow 500 includes rotating the firstplanar refractive component around the coaxial axis to a first selectedposition and rotating the second planar refractive component around thecoaxial axis to a second selected position, wherein the steeredelectromagnetic beam has an azimuth angle θ and a zenith angle φ betweenzero and a finite angle from the coaxial axis. The azimuth angle θ andthe zenith angle φ are responsive to the first deflection angle, thesecond deflection angle, the first selected position, and the secondselected position. In an embodiment, the operational flow includesreceiving information indicative of a position of the target 295, anddetermining the first selected position and the second selected positionpointing the steered electromagnetic beam at the target. In anembodiment, the targeting operation may be implemented using the beamcontroller 480 described in conjunction with FIG. 4. In an embodiment,the receiving includes receiving information indicative of a position ofthe target in a three dimensional space. In an embodiment, theoperational flow includes initiating the electromagnetic beam incidenton the first planar refractive component. In an embodiment, theinitiating may be implemented using the beam generator 486 described inconjunction with FIG. 4.

FIG. 6 illustrates an example electromagnetic beam steering apparatus600 and a reference three-dimensional axis 602. The apparatus includes afirst blazed transmission diffraction grating component 610 configuredto angularly deflect an electromagnetic beam 630 at a first blaze angle634. The apparatus includes a second blazed transmission diffractiongrating component 620 configured to angularly deflect an electromagneticbeam, illustrates as the transmitted electromagnetic beam 632, at asecond blaze angle 638. The apparatus includes an electromagnetic beamsteering structure 650 configured to independently rotate the firstblazed transmission diffraction grating component and the second blazedtransmission diffraction grating component about a coaxial axis 605 suchthat the electromagnetic beam 630 incident on the first blazedtransmission diffraction grating component exits the second blazedtransmission diffraction grating component as a steered electromagneticbeam, illustrated by the second output electromagnetic beam 636. In anembodiment, the electromagnetic beam steering apparatus may steer anelectromagnetic beam in a transmit mode or in a receive mode. Forexample, in an embodiment, the electromagnetic beam steering structuremay function or operate in a Risley prism beam steering manner.

In an embodiment, a diffraction grating (612 or 622) is a collection oftransmitting elements separated by a distance comparable to thewavelength of the electromagnetic beam 630. A diffraction grating may bethought of as a collection of diffracting elements, such as a pattern oftransparent slits or apertures in an opaque screen, or a collection ofreflecting grooves on a substrate. A fundamental physical characteristicof a diffraction grating is a spatial modulation of the refractiveindex. Upon diffraction, an electromagnetic beam incident on a gratingwill have its electric field amplitude, or phase, or both, modified in apredictable manner due to the periodic variation in refractive index inthe region near the surface of the grating. In an embodiment, thediffractive behavior operates by a constructive interference ofelectromagnetic waves transmitted through an amplitude or phase mask. Inan embodiment, a reflection grating consists of a grating superimposedon a reflective surface, and a transmission grating consists of agrating superimposed on a transparent surface.

In an embodiment of a blazed transmission grating (612 or 622) nearlyall of the diffracted or refracted electromagnetic energy is selectivelyconcentrated in a specific angular range, which is referred to as ablaze angle. A blaze angle is a concentrated or efficient deflection ofnearly all the diffracted beam energy by a blazed transmission gratingwithin or at a particular angle, e.g., the blaze angle. Diffractiongratings can be optimized such that most of the power goes into acertain diffraction order, leading to a high diffraction efficiency forthat order. This optimization leads to position-dependent phase changesdescribed by a sawtooth-like function (with linear increases followed bysudden steps). The slope of the corresponding surface profile isoptimized for the given conditions in terms of input angle andwavelength.

In an embodiment, a blazed transmission grating deflects a desireddiffraction order and suppresses other diffraction orders. In anembodiment of a blazed transmission grating most of the transmitted beamwill be diffracted in either the zero-order or a first order. Thedirection in which maximum efficiency is achieved is called the blazeangle and is the third crucial characteristic of a blazed gratingdirectly depending on blaze wavelength and diffraction order. In anembodiment, a blazed transmission grating is optimized to achievemaximum grating efficiency in a selected diffraction order. In anembodiment, a blazed transmission grating may be implemented by a ruledgrating, a holographic grating, or an efficient media grating. The blazeangle of a transmission grating is not the same as a groove angle of aruled grating.

In an embodiment, the electromagnetic beam 630 includes a radiofrequencyelectromagnetic beam. For example, a radiofrequency electromagnetic beammay include a microwave band radiofrequency electromagnetic beam. Forexample, a radiofrequency electromagnetic beam may include a 1 GHz to300 GHz radiofrequency electromagnetic beam. For example, aradiofrequency electromagnetic beam may include a radiofrequencyelectromagnetic beam with a free space wavelength between 30 cm to 1 mm.In an embodiment, the electromagnetic beam includes a light wavelengthelectromagnetic beam. For example, a light wavelength electromagneticbeam may include an infrared or a visible light wavelengthelectromagnetic beam.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes two opposed generally planar and parallel majorsurfaces and a thickness 616 that is less than the free-space wavelengthof the electromagnetic beam 630. In an embodiment, a planar surface ofthe two opposed generally planar and parallel major surfaces has aradius of curvature that is large relative to the thickness. In anembodiment, the radius of curvature is greater than ten times thethickness. In an embodiment, the radius of curvature includes acylindrical radius of curvature. In an embodiment, a major surface 614of the first blazed transmission diffraction grating component 610includes a generally or substantially flat major surface. In anembodiment, a receiving or transmitting surface of the first blazedtransmission diffraction grating component 610 includes an arbitrarysurface approximating a flat surface.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first planar blazed transmission diffractiongrating. In an embodiment, the second blazed transmission diffractiongrating component 620 includes a second planar blazed transmissiondiffraction grating. In an embodiment, the first blazed transmissiondiffraction grating component and the second blazed transmissiondiffraction grating component each have a thickness (616, 626) less thanthe free-space wavelength of the incident electromagnetic beam 630(hereafter free-space subwavelength thickness). In an embodiment, thefree-space subwavelength thickness includes a subwavelength thickness ofless than one-half of the free-space wavelength of the electromagneticbeam. In an embodiment, the free-space subwavelength thickness includesa subwavelength thickness of less than one-fifth of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-tenth of the free-space wavelength of the electromagnetic beam.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 and the second blazed transmission diffraction gratingcomponent 620 are each selected to angularly deflect in combination theincident electromagnetic beam 630 at blaze angles optimized forelectromagnetic beam steering. In an embodiment, the first transmissiondiffraction grating component is optimized to maximize the transmittedelectromagnetic beam 632 energy at the first blaze angle 634 forelectromagnetic beam steering while minimizing the total transmittedelectromagnetic beam energy at the zeroth-order (the unwanted bore sightbeam) and other unwanted orders of the diffracted beam to less thanfifty-percent of the electromagnetic beam energy transmitted at theblaze angle. For example, the minimizing includes suppression of +1order transmitted beam when using −1 order transmitted beam as a “mainlobe.” In an embodiment, the total transmitted electromagnetic beamenergy at the zeroth-order and other unwanted orders of the diffractedbeam are minimized to less than thirty-percent of the electromagneticbeam energy transmitted at the blaze angle. In an embodiment, the firsttransmission diffraction grating component is optimized so that nearlyall the diffracted transmitted beam energy is concentrated in aparticular angle, the first blaze angle. In an embodiment, the firstblaze angle is selected to optimize the transmitted electromagnetic beam632 energy. In an embodiment, the first blaze angle is selected tomaximize the transmitted electromagnetic beam 632 energy with aprincipal intensity maximum at the first blaze angle and minimize thetotal transmitted electromagnetic beam energy at the zeroth-order andother unwanted orders of the diffracted electromagnetic beam. In anembodiment, the first blaze angle and the second blaze angle are eachselected to maximize in combination the transmitted energy of thesteered electromagnetic beam 636 with a principal intensity maximum atthe second blaze angle 638 and minimize the total transmittedelectromagnetic beam energy at the zeroth-order and other unwantedorders of the transmitted electromagnetic beam.

In an embodiment, a characteristic of the first blazed transmissiondiffraction grating component 610 is selected to maximize thetransmitted electromagnetic beam 632 energy at the first blaze angle 634while minimizing the total transmitted electromagnetic beam energy atthe zeroth-order and other unwanted orders of the diffracted beam toless than fifty-percent of the electromagnetic beam energy transmittedat the first blaze angle. For example, the characteristic may include ashape or a spacing of a grating of the first blazed transmissiondiffraction component. In an embodiment, the selected characteristic ofthe first blazed transmission diffraction grating component includes aselected periodicity of diffracting elements of the first blazedtransmission diffraction grating component. In an embodiment, the firstblaze angle 634 of the first blazed transmission diffraction gratingcomponent 610 is selectable by choosing a periodicity of the firstblazed transmission grating. In an embodiment, the periodicity of thefirst blazed transmission grating is established by switching or tuningthe periodicity of a dynamic grating.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first graded-index or a gradient-index blazedtransmission diffraction grating. In an embodiment, the first blazedtransmission diffraction grating component includes a first stronglyasymmetrically shaped refractive index map within one period of thefirst grating component. In an embodiment, the first blazed diffractiongrating transmission component includes a one-dimensional blazedtransmission diffraction grating. For example, a one-dimensional blazedtransmission diffraction grating may include a structural uniformity ina first dimension and no structural uniformity in a second orthogonaldimension, such as a periodic media. In an embodiment, the first blazeddiffraction grating transmission component includes a two-dimensionalblazed transmission diffraction grating. In an embodiment, the firstblazed diffraction grating transmission component includes athree-dimensional blazed transmission diffraction grating.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first blazed transmission diffraction gratingformed by parallel grooves on a substrate. For example, the parallelgrooves may include ruled or laser interference patterns. In anembodiment, the parallel grooves include rectangular-profile parallelgrooves. In an embodiment, the first blazed transmission diffractiongrating component includes a first blazed transmission diffractiongrating formed by wires on a substrate. In an embodiment, the firstblazed transmission diffraction grating component includes a firstholographic transmission diffraction grating.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first linearly varying graded index diffractiontransmission grating configured to angularly deflect an electromagneticbeam at the first blaze angle 634. In an embodiment, the first linearlyvarying graded index diffraction transmission grating includes a firstoptimized linearly varying transverse index profile over a periodicallyrepeated one-dimensional cell configured to angularly deflect theincident electromagnetic beam at a selected first blaze angle. Forexample, a simple linear saw tooth profile may not have the bestpossible gain or side lobe level. Optimization of the transverse indexprofile over a periodically repeated one-dimensional cell addressesthese problems, and it would typically use the simple linear saw toothas an “initial informed guess” starting point.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first blazed transmission diffraction gratingformed by an artificially structured effective media producing orbehaving as a periodically varying refractive index deflecting theelectromagnetic beam 630 at the first blaze angle 634. For example, theperiodically varying refractive index allows the scattered wave front tobe specified essentially at will. For example, the resonant nature ofsubwavelength resonators and unit cells introduces the abrupt phaseshifts, or abrupt changes phase, amplitude, or polarization. In anembodiment, the periodically varying refractive index includes aperiodically varying refractive index producing an abrupt phase,amplitude, or polarization shift over a scale of a wavelength of theelectromagnetic beam. In an embodiment, the phase shift is a function ofa position along the interface. In an embodiment, the phase shift is afunction of abrupt phase changes in the electromagnetic beam path overthe scale of a wavelength. In an embodiment, the periodically varyingrefractive index includes a periodically varying refractive indexproducing a phase discontinuity in the electromagnetic beam. Forexample, a discontinuous phase blazed transmission diffraction grating.In an embodiment, the artificially structured effective media includesan artificially structured subwavelength effective media configured toproduce the periodically varying refractive index. In an embodiment, theartificially structured effective media includes a negative permittivityor negative permeability media configured to produce the periodicallyvarying refractive index. In an embodiment, the artificially structuredeffective media includes artificially structured subwavelengthelectromagnetic unit cells configured to produce the periodicallyvarying refractive index. In an embodiment, the artificially structuredeffective media includes artificially structured subwavelengthmetamaterial unit cells configured to produce the periodically varyingrefractive index. In an embodiment, the artificially structuredeffective media includes an artificially structured meta-surface ormeta-interface having a subwavelength unit structure and configured toproduce the periodically varying refractive index. In an embodiment, theartificially structured effective media includes a metamaterial surfaceconfigured to produce the periodically varying refractive index. In anembodiment, the artificially structured effective media includes ameta-surface, or meta-interface configured to produce the periodicallyvarying refractive index. In an embodiment, the artificially structuredeffective media includes artificially structured metamaterial componentshaving a periodically repeating gradient profile configured to producethe periodically varying refractive index. In an embodiment, theartificially structured effective media includes at least twometamaterial components arranged to produce the periodically varyingrefractive index.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 and the second blazed transmission diffraction gratingcomponent 620 each respectively include a substrate transparent to theelectromagnetic beam 630. In an embodiment, the first blazedtransmission diffraction grating component and the second blazedtransmission diffraction grating component each respectively include asubstrate stretchable along a coaxial axis (X-axis or Y-axis) normal toan axis of the grating. For example, a stretchable substrate is expectedto produce a tunable refractive index to suppress the zero order oranother order of the diffraction across a range of wavelengths.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first blazed transmission diffraction gratinghaving a periodic or modified periodic variation in the refractiveindex. In an embodiment, the first blazed transmission diffractiongrating having a periodic or modified periodic variation in therefractive index includes an artificially structured effective mediapresenting a two-dimensional or a three-dimensional grating to theelectromagnetic beam 630. In an embodiment, the first blazedtransmission diffraction grating having a periodic or modified periodicvariation in the refractive index includes an optimized artificiallystructured effective media presenting two-dimensional pixels to theelectromagnetic wave. In an embodiment, the first blazed transmissiondiffraction grating having a periodic or modified periodic variation inthe refractive index includes an optimized artificially structuredeffective media presenting three-dimensional voxels to theelectromagnetic wave. Examples of artificially structured effectivemedia are described in P. Herman, et al., U.S. Pub. Pat. App.2012/0039567.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes a first achromatic blazed transmissiondiffraction grating component and the second blazed transmissiondiffraction grating component 620 includes a second achromatic blazedtransmission diffraction grating component. Each grating componenthaving a respective tangential refractive index gradient deflecting theelectromagnetic beam 630 at a respective blaze angle over a finite rangeof wavelengths. For example, a finite range of wavelengths includes adiscrete set of wavelengths. In an embodiment, the first achromaticblazed transmission component produces an anomalous dispersion of theelectromagnetic beam at the blaze angle over a first finite range ofwavelengths. For example, the first achromatic blazed transmissioncomponent may produce a dispersive phase compensation cancelling thewavelength dependence of the diffraction phenomena with complementarydispersion. In an embodiment, the first achromatic blazed transmissioncomponent includes a planar refractive component and an amplitude orphase grating combined to form a single achromatic component. In anembodiment, the first achromatic blazed transmission component includesa negatively sloped refractive index as a function of frequency(dn/df<0). In an embodiment, the first achromatic blazed transmissioncomponent includes an artificial media having a negatively slopedrefractive index as a function of frequency (dn/df<0). In an embodiment,the first achromatic blazed transmission component includes a firstachromatic blazed transmission component having effective negativepermittivity or negative permeability media achromatically diffractingan electromagnetic beam at the first blaze angle over a finite range ofwavelengths. In an embodiment, the first achromatic blazed transmissioncomponent includes a first achromatic blazed transmission componenthaving an effective negative permittivity or negative permeability mediaachromatically diffracting an electromagnetic beam at the first blazeangle over a finite range of wavelengths. In an embodiment, the firstachromatic blazed transmission component includes a composite ofsubwavelength materials having an effective negative permittivity ornegative permeability diffracting an electromagnetic beam at the firstblaze angle over a finite range of wavelengths. In an embodiment, thecomposite of subwavelength materials includes at least one subwavelengthresonator. In an embodiment, the at least one subwavelength resonatorincludes at least one metamaterial unit cell. In an embodiment, thecomposite of subwavelength materials includes at least one deeplysubwavelength element. In an embodiment, the composite of subwavelengthmaterials includes at least two subwavelength components havingdifferent electromagnetic beam dispersion characteristics. In anembodiment, the composite of subwavelength materials includes at leastthree subwavelength components having a varying spacing.

In an embodiment, the first blazed transmission diffraction gratingcomponent 610 includes an artificially structured effective media havingan electronically-selectable blaze angle 634 deflecting theelectromagnetic beam 630 at a first blaze angle if in a first state anda deflecting the electromagnetic beam at a second blaze angle if in asecond state. For example, the artificially structured effective mediamay include a binary media. In an embodiment, the first state is an“off-state” and the second state is an “on-state.” In an alternativeembodiment, the artificially structured effective media may be acomposite structure having a first grating subcomponent having a firstblaze gradient deflecting the electromagnetic beam at a first blazeangle and a second grating subcomponent having the electronicallyselectable second refractive gradient. This composite structure providestwo different selectable tangential refractive index gradients.

In an embodiment, the electromagnetic beam steering structure 650includes an electronically controlled electromagnetic beam steeringstructure. In an embodiment, the electromagnetic beam steering structureis configured to independently rotate or counter rotate the first blazedtransmission diffraction grating component 610 and the second blazedtransmission diffraction grating component relative to the coaxial axis605. In an embodiment, the electromagnetic beam steering structure isconfigured to rotate the first blazed transmission diffraction gratingcomponent and the second blazed transmission diffraction gratingcomponent about the coaxial axis while maintaining an electromagneticbeam path or alignment through the first blazed transmission diffractiongrating component and the second blazed transmission diffraction gratingcomponent.

In an embodiment, the steered electromagnetic beam 636 has directionthat is a vector sum of the first blaze angle 634 of the first blazedtransmission diffraction grating component 610 and the second blazeangle 638 of the second blazed transmission diffraction gratingcomponent 620. In an embodiment, the electromagnetic beam 630 incidenton the first blazed transmission diffraction grating component exits thesecond blazed transmission diffraction grating component as the steeredelectromagnetic beam 636 having a direction (azimuth angle θ 639 andzenith angle φ, illustrated by the second deflection angle 638) that isa vector sum of the first deflection angle of the first blazedtransmission diffraction grating component and the second deflectionangle of the second blazed transmission diffraction grating component.In an embodiment, the steered electromagnetic beam has a controllabletilt at an angle φ relative to the coaxial axis. In an embodiment, thesteered electromagnetic beam has a controllable rotation at an azimuthangle θ about the coaxial axis 605. In an embodiment, theelectromagnetic beam steering structure is configured to steer theelectromagnetic beam 630 propagating along the coaxial axis normal tothe first blazed transmission diffraction grating component and thesecond blazed transmission diffraction grating component to an azimuthangle θ and a zenith angle φ between zero and a finite angle from thecoaxial axis. In an embodiment, the electromagnetic beam steeringstructure is configured to steer the electromagnetic beam to aselectable portion of a field of regard. In an embodiment, theelectromagnetic beam steering structure is configured to steer theelectromagnetic beam within a continuous range of directions within afield of regard.

In an embodiment, the apparatus 600 includes a beam controller 680configured to calculate a rotational position of the first blazedtransmission diffraction grating 610 component about the coaxial axis605 and a rotational position of the second blazed transmissiondiffraction grating component 620 pointing the steered electromagneticbeam 636 at the selected target 295. In an embodiment, the apparatus 600includes an electromagnetic beam generator 686 configured to transmitthe electromagnetic beam 630.

Various embodiments or variations of the first blazed transmissiondiffraction grating component 610 are described herein. In anembodiment, the second blazed transmission diffraction grating component620 may include one or more of the embodiments or variations describedfor the first planar refractive component. For example, the secondblazed transmission grating may include a major surface 624.

FIG. 7 illustrates an example operational flow 700. After a startoperation, the operational flow includes a first deflecting operation710. The first deflecting operation includes passing an electromagneticbeam through a first blazed transmission diffraction grating componentconfigured to angularly deflect the electromagnetic beam at a firstblaze angle relative to a coaxial axis, and generating a first outputelectromagnetic beam. In an embodiment, the first deflecting operationmay be implemented by passing the electromagnetic beam 630 through thefirst blazed transmission diffraction grating component 610 configuredto angularly deflect the electromagnetic beam at the first blaze angle634 relative to the coaxial axis 605, and generating a first outputelectromagnetic beam 632 described in conjunction with FIG. 6. A seconddeflecting operation 720 includes passing the first outputelectromagnetic beam through a second blazed transmission diffractiongrating component configured to angularly deflect the first outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis and generating a steered electromagnetic beam. In an embodiment,the second deflecting operation may be implemented by passing the firstoutput electromagnetic beam 632 through the second blazed transmissiondiffraction grating component 620 configured to angularly deflect thefirst output electromagnetic beam at the second blaze angle 638 relativeto the coaxial axis 605 and generate the steered electromagnetic beam436 described in conjunction with FIG. 6. The steered electromagneticbeam having a direction relative to the coaxial axis that is a vectorsum of the first blaze angle and the second blaze angle. The operationalflow includes an end operation. In an embodiment, the first blazedtransmission diffraction grating component includes an artificiallystructured effective media configured to angularly deflect an incidentelectromagnetic beam at a first blaze angle.

In an embodiment, the operational flow 700 includes rotating the firstblazed transmission diffraction grating component around the coaxialaxis to a first selected position, and rotating the second blazedtransmission diffraction grating component around the coaxial axis to asecond selected position. The steered electromagnetic beam has anazimuth angle θ (rotation about the coaxial axis) and a zenith angle φ(deflection from the coaxial axis) between zero and a finite angle fromthe coaxial axis. The azimuth angle θ and the zenith angle φ areresponsive to the first blaze angle, the second blaze angle, the firstselected position, and the second selected position. In an embodiment,the operational flow includes receiving information indicative of aposition of a target in a three dimensional space, and determining thefirst selected position and the second selected position pointing thesteered electromagnetic beam at the target. In an embodiment, theoperational flow includes initiating the electromagnetic beam incidenton the first blazed transmission diffraction grating component.

FIG. 8 illustrates an example electromagnetic beam steering apparatus800 and a reference three-dimensional axis 802. The electromagnetic beamsteering apparatus includes a first blazed transmission diffractiongrating component 810 having a first volumetric distribution ofdielectric constants 812 configured to angularly deflect anelectromagnetic beam 830 at a first blaze angle 834. The electromagneticbeam steering apparatus includes a second blazed transmissiondiffraction grating component 820 having a second volumetricdistribution of dielectric constants 822 configured to angularly deflectelectromagnetic beam 832 at a second blaze angle 838. Theelectromagnetic beam steering apparatus includes an electromagnetic beamsteering structure configured to independently rotate the first blazedtransmission diffraction grating component and the second blazedtransmission diffraction grating component about a coaxial axis 805 suchthat an electromagnetic beam 830 incident on the first blazedtransmission diffraction grating component exits the second blazedtransmission diffraction grating component as a steered electromagneticbeam 836.

In an embodiment, the first volumetric distribution of dielectricconstants 812 is divided into a plurality of sub-wavelength voxelshaving a maximum dimension of less than half of a wavelength of theelectromagnetic beam, and each voxel is assigned one of a plurality ofdielectric constants to approximate the first volumetric distribution ofdielectric constants. In an embodiment, the first volumetricdistribution of dielectric constants is approximated using one or morediscrete materials having specific dielectric constants. In anembodiment, the second volumetric distribution of dielectric constants822 is divided into a plurality of sub-wavelength voxels having amaximum dimension of less than half of a wavelength of theelectromagnetic beam, and each voxel is assigned one of a plurality ofdielectric constants to approximate the second volumetric distributionof dielectric constants. In an embodiment, the second volumetricdistribution of dielectric constants is approximated using one or morediscrete materials having specific dielectric constants.

In an embodiment, the first blazed transmission diffraction gratingcomponent 810 and the second blazed transmission diffraction gratingcomponent 820 have substantially similar volumetric distribution ofdielectric constants. In an embodiment, the first blazed transmissiondiffraction grating component and the second blazed transmissiondiffraction grating component have dissimilar volumetric distributionsof dielectric constants.

In an embodiment, the first volumetric distribution of dielectricconstants 812 is selected based on an equation for a holographicsolution. In an embodiment, the first volumetric distribution ofdielectric constants is selected using an optimization algorithm inwhich the dielectric constants are treated as optimizable variables. Inan embodiment, the dielectric constants are binary (0, 1). For example,binary dielectric constants are easier to three-dimensionally print. Inan embodiment, the dielectric constants are a quasi-continuous grayscale with a range from a minimum to a maximum value, for example 1-10.A goal in optimizing the first volumetric distribution of dielectricconstants is to minimize a deviation between a goal or desired firstblaze angle and an achievable or actual blaze angle. In an embodiment,standard optimization techniques may be used. For example, least squaresmethodology may be used to minimize a deviation between a goal ordesired first blaze angle and an achievable or actual first blaze angle.In an embodiment, the real and imaginary parts of the dielectricconstants are treated as individually optimizable variables. In anembodiment, the optimization algorithm includes modifying at least oneoptimizable variable and determining a cost function for themodification. In an embodiment, the optimization algorithm includesdetermining a gradient of the cost function based on its partialderivatives with respect to each of the optimizable variables. In anembodiment, the optimization algorithm includes determining asensitivity vector of a given configuration using an adjoint sensitivityalgorithm. In an embodiment, the optimization algorithm comprises aconstrained optimization algorithm in which the dielectric constants aretreated as optimization variables constrained to have real parts greaterthan or equal to approximately one and imaginary parts equal to orapproximately zero. In an embodiment, the optimization algorithmincludes starting with an initial guess corresponding to a solution.Example optimization algorithms are described in U.S. patent applicationSer. No. 14/638,961, entitled HOLOGRAPHIC MODE CONVERSION FORELECTROMAGNETIC RADIATION, naming Tom Driscoll et al. as inventors,filed Mar. 4, 2015.

In an embodiment, the first blazed transmission diffraction gratingcomponent 810 includes two opposed generally planar and parallel majorsurfaces and a thickness 816 that is less than the free-space wavelengthof the electromagnetic beam 830. In an embodiment, a planar surface ofthe two opposed generally planar and parallel major surfaces has aradius of curvature that is large relative to the thickness. In anembodiment, the radius of curvature is greater than ten times thethickness. In an embodiment, the radius of curvature includes acylindrical radius of curvature. In an embodiment, a major surface 814of the first blazed transmission diffraction grating component 810includes a generally or substantially flat major surface. In anembodiment, a receiving or transmitting surface of the first blazedtransmission diffraction grating component 810 includes an arbitrarysurface approximating a flat surface.

In an embodiment, the first blazed transmission diffraction gratingcomponent 810 includes a first planar blazed transmission diffractiongrating. In an embodiment, the second blazed transmission diffractiongrating component 820 includes a second planar blazed transmissiondiffraction grating. In an embodiment, the first blazed transmissiondiffraction grating component and the second blazed transmissiondiffraction grating component each have a thickness (816, 826) less thanthe free-space wavelength of the incident electromagnetic beam 830(hereafter free-space subwavelength thickness). In an embodiment, thefree-space subwavelength thickness includes a subwavelength thickness ofless than one-half of the free-space wavelength of the electromagneticbeam. In an embodiment, the free-space subwavelength thickness includesa subwavelength thickness of less than one-fifth of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-tenth of the free-space wavelength of the electromagnetic beam.

In an embodiment, the electromagnetic beam steering structure 850includes an electronically controlled electromagnetic beam steeringstructure. In an embodiment, the electromagnetic beam steering structureis configured to independently rotate or counter rotate the first blazedtransmission diffraction grating component 810 and the second blazedtransmission diffraction grating component 820 relative to the coaxialaxis. In an embodiment, the electromagnetic beam steering structure isconfigured to rotate the first blazed transmission diffraction gratingcomponent and the second blazed transmission diffraction gratingcomponent about the coaxial axis 805 while maintaining anelectromagnetic beam path or alignment through the first blazedtransmission diffraction grating component and the second blazedtransmission diffraction grating component.

In an embodiment, the steered electromagnetic beam 836 has directionthat is a vector sum of the first blaze angle 834 of the first blazedtransmission diffraction grating component 810 and the second blazeangle 838 of the second blazed transmission diffraction gratingcomponent 820. In an embodiment, the electromagnetic beam 830 incidenton the first blazed transmission diffraction grating component exits thesecond blazed transmission diffraction grating component as a steeredelectromagnetic beam 836 having a direction (azimuth angle θ 839 andzenith angle φ, illustrated by the second blaze angle 838) that is avector sum of the first deflection angle of the first blazedtransmission diffraction grating component and the second deflectionangle of the second blazed transmission diffraction grating component.In an embodiment, the steered electromagnetic beam has a controllabletilt at an angle φ relative to the coaxial axis 805. In an embodiment,the steered electromagnetic beam has a controllable rotation at anazimuth angle θ about the coaxial axis 805. In an embodiment, theelectromagnetic beam steering structure is configured to steer theelectromagnetic beam 830 propagating along the coaxial axis normal tothe first blazed transmission diffraction grating component and thesecond blazed transmission diffraction grating component to an azimuthangle θ and a zenith angle φ between zero and a finite angle from thecoaxial axis. In an embodiment, the electromagnetic beam steeringstructure is configured to steer the electromagnetic beam to aselectable portion of a field of regard. In an embodiment, theelectromagnetic beam steering structure is configured to steer theelectromagnetic beam within a continuous range of directions within afield of regard.

In an embodiment, the apparatus 800 includes a beam controller 880configured to calculate a rotational position of the first blazedtransmission diffraction grating component 810 about the coaxial axis805 and a rotational position of the second blazed transmissiondiffraction grating component about the coaxial axis pointing thesteered electromagnetic beam at the selected target 295. In anembodiment, the apparatus includes an electromagnetic beam generatorconfigured to transmit the electromagnetic beam.

Various embodiments or variations of the first blazed transmissiondiffraction grating component 810 are described herein. In anembodiment, the second blazed transmission diffraction grating component820 may include one or more of the embodiments or variations describedfor the first planar refractive component. For example, the secondblazed transmission grating may include a major surface 824.

FIG. 9 illustrates an example operational flow 900. After a startoperation, the operational flow includes a first deflection operation910. The first deflection operation includes passing an electromagneticbeam through a first blazed transmission diffraction grating componenthaving a first volumetric distribution of dielectric constantsconfigured to angularly deflect the electromagnetic beam at a firstblaze angle relative to a coaxial axis, and generating a first outputelectromagnetic beam. In an embodiment, the first deflection operationmay be implemented by passing the electromagnetic beam 830 through thefirst blazed transmission diffraction grating component 810 having thefirst volumetric distribution of dielectric constants 812 configured toangularly deflect the electromagnetic beam at the first blaze angle 834relative to the coaxial axis 805, and generating the first outputelectromagnetic beam 832 as described in conjunction with FIG. 8. Asecond deflection operation 920 includes passing the first outputelectromagnetic beam through a second blazed transmission diffractiongrating component having a second volumetric distribution of dielectricconstants configured to angularly deflect the first outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis and generating a steered electromagnetic beam. The steeredelectromagnetic beam having a direction relative to the coaxial axisthat is a vector sum of the first blaze angle and the second blazeangle. In an embodiment, the second deflection operation may beimplemented by passing the first output electromagnetic beam 832 throughthe second blazed transmission diffraction grating component 820 havingthe second volumetric distribution of dielectric constants 822configured to angularly deflect the first output electromagnetic beam atthe second blaze angle 838 relative to the coaxial axis and generatingthe steered electromagnetic beam 836 as described in conjunction withFIG. 8. The operational flow includes an end operation.

In an embodiment, the first deflection operation 910 includes passing anelectromagnetic beam through a first blazed transmission diffractiongrating component having a first volumetric distribution of dielectricconstants, wherein the first volumetric distribution of dielectricconstants are divided into a plurality of sub-wavelength voxels having amaximum dimension of less than half of the wavelength of theelectromagnetic beam, and each voxel assigned one of a plurality ofdielectric constants to approximate the first volumetric distribution ofdielectric constants. In an embodiment, the second deflection operation920 includes passing the first output electromagnetic beam through asecond blazed transmission diffraction grating component having a secondvolumetric distribution of dielectric constants, wherein the secondvolumetric distribution of dielectric constants divided into a pluralityof sub-wavelength voxels having a maximum dimension of less than half ofa wavelength of the electromagnetic beam frequency, and each voxelassigned one of a plurality of dielectric constants to approximate thesecond volumetric distribution of dielectric constants.

In an embodiment, the operational flow 900 includes rotating the firstblazed transmission diffraction grating component around the coaxialaxis to a first selected position, and rotating the second blazedtransmission diffraction grating component around the coaxial axis to asecond selected position. The steered electromagnetic beam has anazimuth angle θ and a zenith angle φ between zero and a finite anglefrom the coaxial axis. The azimuth angle θ and the zenith angle φ areresponsive to the first blaze angle, the second blaze angle, the firstselected position, and the second selected position. In an embodiment,the operational flow includes receiving information indicative of aposition of the target 295 in a three dimensional space, and determiningthe first selected position and the second selected position pointingthe steered electromagnetic beam at the target. In an embodiment, theoperational flow includes initiating the electromagnetic beam incidenton the first blazed transmission diffraction grating component.

FIG. 10 illustrates an example dual-channel electromagnetic beamsteering apparatus 1000 and a reference three-dimensional axis 1002. Theapparatus includes a first dual-channel blazed transmission diffractiongrating component 1010 having a first volumetric distribution ofdielectric constants 1012 configured to deflect at a first blaze angle1034 (i) a first electromagnetic beam 1030 f0 having a first frequencyand (ii) a second electromagnetic beam 1030 f1 having a secondfrequency. In an embodiment, the first frequency includes a firstoperational channel or a first service band. In an embodiment, thesecond frequency includes a second operational channel or a secondservice band. The apparatus includes a second dual-channel blazedtransmission diffraction grating component 1020 including a secondvolumetric distribution of dielectric constants 1022 configured todeflect at a second blaze angle 1038 (i) the first electromagnetic beam1030 f0 having a first frequency and (ii) the second electromagneticbeam 1030 f1 having a second frequency. The apparatus includes anelectromagnetic beam steering structure 1050 configured to independentlyrotate the first dual-channel blazed transmission diffraction gratingcomponent and second dual-channel blazed transmission diffractiongrating component about a coaxial axis 1005 such that the first andsecond electromagnetic beams incident on the first dual-channel blazedtransmission diffraction grating component exit the second dual-channelblazed transmission diffraction grating component as steered first andsecond electromagnetic beams.

In an embodiment, the first volumetric distribution of dielectricconstants 1012 are divided into a first plurality of sub-wavelengthvoxels having a maximum dimension of less than half of a wavelength ofthe first frequency or the second frequency, and each voxel is assignedone of a plurality of dielectric constants to approximate the firstvolumetric distribution of dielectric constants 1022. In an embodiment,the second volumetric distribution of dielectric constants are dividedinto a second plurality of sub-wavelength voxels having a maximumdimension less than half of a wavelength of the first frequency or thesecond frequency, and each voxel is assigned one of a plurality ofdielectric constants to approximate the second volumetric distributionof dielectric constants.

Various embodiments or variations of the first dual-channel blazedtransmission diffraction grating component 1010 are described herein. Inan embodiment, the second dual-channel blazed transmission diffractiongrating component 1020 may include one or more of the embodiments orvariations described for the first planar refractive component. Forexample, the second blazed transmission grating may include a majorsurface 1024.

FIGS. 11 and 12 illustrate modeling results for a dual-channel blazedtransmission diffraction grating component having a volumetricdistribution of dielectric constants configured to deflect at a blazeangle for example such as the first dual-channel blazed transmissiondiffraction grating component 1010 or the second dual-channel blazedtransmission diffraction grating component 1020 of FIG. 10. The modelingwas performed using Compsol Multiphysics® Modeling Software, with f0being 10 GHz and f1 being 8.75 GHz. FIG. 11 illustrates a volumetricdistribution of dielectric constants in a dual-channel blazedtransmission diffraction grating component configured to deflect anelectromagnetic beam at a specified blaze angle. FIG. 12A illustrates adeflection of the first electromagnetic beam 1030 f0 at a selected blazeangle, illustrated as the first blaze angle 1034. FIG. 12B illustrates adeflection of the second electromagnetic beam 1030 f1 at the selectedblaze angle, illustrated as the first blaze angle 1034.

The modeling results illustrated in FIGS. 11 and 12 demonstrate that adual-channel blazed transmission diffraction grating component having avolumetric distribution of dielectric constants defining a constantrefractive index is achievable using low-loss dielectrics with adielectric permittivity ranging between one and about two. In anembodiment, a dual-channel electromagnetic beam steering apparatus mayimplement a frequency duplexing electromagnetic communications system.For example, a satellite communications system, an air-to-ground system,or an LTE system that use one channel for uplink and another channel fordownlink may be implement using the dual-channel electromagnetic beamsteering apparatus 1000.

In an embodiment, the second frequency is not less than 87.5% of thefirst frequency. In an embodiment, the second frequency is not less than90% of the first frequency. In an embodiment, the second frequency isnot less than 92.5% of the first frequency.

In an embodiment, the first volumetric distribution of dielectricconstants 1012 is approximated using one or more discrete materialshaving specific dielectric constants. In an embodiment, the firstdual-channel blazed transmission diffraction grating component 1010 andthe second dual-channel blazed transmission diffraction gratingcomponent 1020 have substantially similar volumetric distributions ofdielectric constants (1012 and 1022). In an embodiment, the firstdual-channel blazed transmission diffraction grating component and thesecond dual-channel blazed transmission diffraction grating componenthave dissimilar volumetric distributions of dielectric constants. In anembodiment, the first volumetric distribution of dielectric constants isselected based on an equation for a holographic solution.

In an embodiment, the first volumetric distribution of dielectricconstants 1012 is selected using an optimization algorithm in which thedielectric constants are treated as optimizable variables. In anembodiment, the dielectric constants are binary (0, 1). For example,binary dielectric constants are easier to three-dimensionally print. Inan embodiment, the dielectric constants are a quasi-continuous grayscale with a range from a minimum to a maximum value, for example 1-10.A goal in optimizing the first volumetric distribution of dielectricconstants is to minimize a deviation between a goal or desired powerdistribution at a first blaze angle and an achievable or actual powerdistribution at the first blaze angle for both the first frequency andthe second frequency. In an embodiment, standard optimization techniquesmay be used. For example, least squares methodology may be used tominimize a deviation between a goal or desired first blaze angle and anachievable or actual first blaze angle for the first frequency and thesecond frequency. In an embodiment, the real and imaginary parts of thedielectric constants are treated as individually optimizable variables.In an embodiment, the optimization algorithm includes modifying at leastone optimizable variable and determining a cost function for themodification. In an embodiment, the optimization algorithm includesdetermining a gradient of the cost function based on its partialderivatives with respect to each of the optimizable variables. In anembodiment, the optimization algorithm includes determining asensitivity vector of a given configuration using an adjoint sensitivityalgorithm. In an embodiment, the optimization algorithm comprises aconstrained optimization algorithm in which the dielectric constants aretreated as optimization variables constrained to have real parts greaterthan or equal to approximately one and imaginary parts equal to orapproximately zero. In an embodiment, the optimization algorithmincludes starting with an initial guess corresponding to a solution.Example optimization algorithms are described U.S. patent applicationSer. No. 14/638,961, entitled HOLOGRAPHIC MODE CONVERSION FORELECTROMAGNETIC RADIATION, naming Tom Driscoll et al. as inventors,filed Mar. 4, 2015.

In an embodiment, the first dual-channel blazed transmission diffractiongrating component 1010 includes two opposed generally planar andparallel major surfaces and a thickness 1016 that is less than thefree-space wavelength of the electromagnetic beam 1030. In anembodiment, a major surface 1014 of the first dual-channel blazedtransmission diffraction grating component 1010 includes a generally orsubstantially flat major surface. In an embodiment, a receiving ortransmitting surface of the first dual-channel blazed transmissiondiffraction grating component 1010 includes an arbitrary surfaceapproximating a flat surface.

In an embodiment, the first dual-channel blazed transmission diffractiongrating component 1010 includes a first dual-channel planar blazedtransmission diffraction grating. In an embodiment, the seconddual-channel blazed transmission diffraction grating component 1020includes a second dual-channel blazed transmission diffraction grating.In an embodiment, the first dual-channel blazed transmission diffractiongrating component and the second dual-channel blazed transmissiondiffraction grating component each have a thickness (1016, 1026) lessthan the free-space wavelength of the incident electromagnetic beam 1030(hereafter free-space subwavelength thickness). In an embodiment, thefree-space subwavelength thickness includes a subwavelength thickness ofless than one-half of the free-space wavelength of the electromagneticbeam. In an embodiment, the free-space subwavelength thickness includesa subwavelength thickness of less than one-fifth of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-tenth of the free-space wavelength of the electromagnetic beam.

In an embodiment, the electromagnetic beam steering structure 1050includes an electronically controlled electromagnetic beam steeringstructure. In an embodiment, the electromagnetic beam steering structureis configured to independently rotate or counter rotate the firstdual-channel blazed transmission diffraction grating component 1010 andthe second dual-channel blazed transmission diffraction gratingcomponent 1020 relative to the coaxial axis 1005. In an embodiment, theelectromagnetic beam steering structure is configured to rotate thefirst dual-channel blazed transmission diffraction grating component andthe second dual-channel blazed transmission diffraction gratingcomponent about the coaxial axis while maintaining an electromagneticbeam path or alignment through the first dual-channel blazedtransmission diffraction grating component and the second dual-channelblazed transmission diffraction grating component.

In an embodiment, the apparatus 1000 includes a beam controller 1080configured to calculate a rotational position of the first dual-channelblazed transmission diffraction grating component 1010 about the coaxialaxis 1005 and a rotational position of the second dual-channel blazedtransmission diffraction grating component 1020 pointing the steeredelectromagnetic beam at the selected target 295. In an embodiment, theapparatus includes an electromagnetic beam generator 1086 configured totransmit the electromagnetic beam 1030.

Various embodiments or variations of the first dual-channel blazedtransmission diffraction grating component 1010 are described herein. Inan embodiment, the second dual-channel blazed transmission diffractiongrating component 1020 may include one or more of the embodiments orvariations described for the first dual-channel blazed transmissiondiffraction grating component 1010.

FIG. 13 illustrates an example operational flow 1100. After a startoperation, the operational flow includes a first deflection operation1110. The first deflection operation includes passing a first incidentelectromagnetic beam having a first frequency or a second incidentelectromagnetic beam having a second frequency through a firstdual-channel blazed transmission diffraction grating component having afirst volumetric distribution of dielectric constants deflecting thefirst incident electromagnetic beam or the second incidentelectromagnetic beam at a first blaze angle relative to a coaxial axis,and generating a first output electromagnetic beam having the firstfrequency or a second output electromagnetic beam having the secondfrequency. In an embodiment, the first deflection operation may beimplemented by passing the first incident electromagnetic beam 1030 f0having a first frequency or a second incident electromagnetic beam 1030f1 having a second frequency through the first dual-channel blazedtransmission diffraction grating component 1010 having the firstvolumetric distribution of dielectric constants 1012 deflecting thefirst incident electromagnetic beam or the second incidentelectromagnetic beam at the first blaze angle 1034 relative to thecoaxial axis 1005, and generating the first output electromagnetic beam1032 f0 having the first frequency or the second output electromagneticbeam 1032 f1 having the second frequency as described in conjunctionwith FIG. 10.

A second deflection operation 1120 includes passing the first outputelectromagnetic beam or the second output electromagnetic beam through asecond dual-channel blazed transmission diffraction grating componenthaving a second volumetric distribution of dielectric constantsdeflecting the first output electromagnetic beam or the second outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis, and generating a first steered electromagnetic beam having thefirst frequency or a second steered electromagnetic beam having thesecond frequency. The first steered electromagnetic beam and the secondsteered electromagnetic beam both having a direction relative to thecoaxial axis that is a vector sum of the first blaze angle and thesecond blaze angle. In an embodiment, the second deflection operationmay be implemented by passing the first output electromagnetic beam 1032f0 or the second output beam 1032 f1 through a second dual-channelblazed transmission diffraction grating component 1020 having a secondvolumetric distribution of dielectric constants deflecting the firstoutput electromagnetic beam or the second output beam at a second blazeangle 1038 relative to the coaxial axis 1005, and generating the firststeered electromagnetic beam 1036 having the first frequency or thesecond steered electromagnetic beam having the second frequency asdescribed in conjunction with FIG. 10. The operational flow includes anend operation.

In an embodiment, the first volumetric distribution of dielectricconstants are divided into a first plurality of sub-wavelength voxelshaving a maximum dimension less than half of a wavelength of the firstfrequency or the second frequency, and each voxel is assigned one of aplurality of dielectric constants to approximate the first volumetricdistribution of dielectric constants. In an embodiment, the secondvolumetric distribution of dielectric constants are divided into asecond plurality of sub-wavelength voxels having a maximum dimensionless than half of a wavelength of the first frequency or the secondfrequency, and each voxel is assigned one of a plurality of dielectricconstants to approximate the second volumetric distribution ofdielectric constants.

In an embodiment of the first deflection operation 1110, the passing afirst electromagnetic beam includes passing a first electromagnetic beamhaving a first frequency and a second electromagnetic beam having asecond frequency through the first dual-channel blazed transmissiondiffraction grating component having a first volumetric distribution ofdielectric constants. In an embodiment of the second deflectionoperation 1120, the passing the first output electromagnetic beamincludes passing the first output electromagnetic beam and the secondoutput beam through the second dual-channel blazed transmissiondiffraction grating component.

In an embodiment, the operational flow 1100 includes rotating the firstdual-channel blazed transmission diffraction grating component aroundthe coaxial axis to a first selected position and rotating the seconddual-channel blazed transmission diffraction grating component aroundthe coaxial axis to a second selected position. The first steeredelectromagnetic beam and the second steered electromagnetic beam eachhave an azimuth angle θ and a zenith angle φ between zero and a finiteangle from the coaxial axis. The azimuth angle θ and the zenith angle φare responsive to the first blaze angle, the second blaze angle, thefirst selected position, and the second selected position. In anembodiment, the operational flow includes receiving informationindicative of a position of a target in a three dimensional space, anddetermining the first selected position and the second selected positionpointing the steered electromagnetic beam at the target 295. In anembodiment, the operational flow includes initiating the firstelectromagnetic beam or the second electromagnetic beam incident on thefirst dual-channel blazed transmission diffraction grating component.

FIG. 14 illustrates an example electromagnetic beam steering apparatus1200 and a reference three-dimensional axis 1202. The electromagneticbeam steering apparatus includes a first electromagnetic beam deflectingstructure 1210 including a first artificially structured effective media1212 having at least two first electronically-selectable or controllabletangential refractive index gradients deflecting an electromagnetic beam1230 incident on the first electromagnetic beam deflecting structure ata first deflection angle 1234, and generating a first outputelectromagnetic beam 1232. The first deflection angle is responsive toan electronically-selected linear refraction gradient of the at leasttwo first electronically selectable tangential refractive indexgradients. The electromagnetic beam steering apparatus includes a secondelectromagnetic beam deflecting structure 1220 including a secondartificially structured effective media 1222 having at least two secondelectronically-selectable or controllable tangential refractive indexgradients deflecting an electromagnetic beam incident on the secondelectromagnetic beam deflecting structure at a second deflection angle1238. The second deflection angle is responsive to anelectronically-selected linear refraction gradient of the at least twosecond electronically selectable tangential refractive index gradients.

In an embodiment, the first electromagnetic beam deflecting structure1210 includes a first planar electromagnetic beam deflecting structure.In an embodiment, the second electromagnetic beam deflecting structure1220 includes a second planar electromagnetic beam deflecting structure.

In an embodiment, the first electromagnetic beam deflecting structure1210 or the second electromagnetic beam deflecting structure 1220 have athickness 1216 and 1226 respectively that is less than the free-spacewavelength of the incident electromagnetic beam 1230 (hereafterfree-space subwavelength thickness). In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-half of the free-space wavelength of the electromagnetic beam. In anembodiment, the free-space subwavelength thickness includes asubwavelength thickness of less than one-fifth of the free-spacewavelength of the electromagnetic beam. In an embodiment, the free-spacesubwavelength thickness includes a subwavelength thickness of less thanone-tenth of the free-space wavelength of the electromagnetic beam.

In an embodiment, the first electromagnetic beam deflecting structure1210 includes a first sub-instance of artificially structured effectivemedia having a fixed tangential refractive index gradient and a secondsub-instance of an individually electronically controlled artificiallystructured effective media having an electronically-selectabletangential refractive index gradient. The fixed tangential refractiveindex gradient and the electronically-selectable tangential refractiveindex gradient in combination deflecting an electromagnetic beam 1230incident on the first electromagnetic beam deflecting structure at anelectronically-selectable first deflection angle 1234. In an embodiment,the first electromagnetic beam deflecting structure includes a firstsub-instance of artificially structured effective media having a fixedtangential refractive index gradient and a second sub-instance of anindividually electronically controlled artificially structured effectivemedia having an electronically-variable refractive index. The fixedtangential refractive index gradient and the electronically-variablerefractive index in combination deflecting an electromagnetic beamincident on first electromagnetic beam deflecting structure at anelectronically-variable first deflection angle. In an embodiment, thefirst electromagnetic beam deflecting structure includes anelectronically-selectable piecewise linear refractive index deflectingan electromagnetic beam incident on the first electromagnetic beamdeflecting structure at a first deflection angle responsive to anelectronically-selected piecewise linear refractive index. In anembodiment, the first electromagnetic beam deflecting structure includesa blazed transmission diffraction grating having at least twoelectronically selectable blaze angles. In an embodiment, the firstelectromagnetic beam deflecting structure includes a composition of atleast two sub-instances of individually electronically controlledartificially structured effective media. Each sub-instance ofindividually electronically controlled artificially structured effectivemedia having a respective tangential refractive index gradient angularlydeviating an electromagnetic beam at a first deflection angle if in afirst state, for example an “on-state,” and angularly deviating anelectromagnetic beam at a second deflection angle if in a second state,for example an “off-state.” In an embodiment, the first electromagneticbeam deflecting structure includes a composite structure of a firstsub-instance of artificially structured effective media having atangential refractive index gradient deflecting an electromagnetic beamat a first blaze angle and a second sub-instance of individuallyelectronically controlled artificially structured effective media havinga tangential refractive index gradient deflecting an electromagneticbeam at a second deflection angle if in a first state and angularlydeviating an electromagnetic beam at a third deflection angle if in asecond state.

In an embodiment, the first electromagnetic beam deflecting structure1210 and the second electromagnetic beam deflecting structure 1220 arein a fixed spatial relationship to each other with planes described bytheir respective deflection angles in a substantially orthogonalrelationship to each other.

In an embodiment, the apparatus 1200 includes a beam controller 1280configured to select a first electronically-selectable or controllabletangential refractive index gradient from the at least two firstelectronically-selectable or controllable tangential refractive indexgradients and a second electronically-selectable or controllabletangential refractive index gradient from the at least two firstelectronically-selectable or controllable tangential refractive indexgradients pointing the steered electromagnetic beam at the selectedtarget 295. In an embodiment, the beam controller is further configuredto initiate the selected first electronically-selectable or controllabletangential refractive index gradient and the selected secondelectronically-selectable or controllable tangential refractive indexgradient.

In an embodiment, the apparatus 1200 includes a positioning structure1255 configured to maintain the first electromagnetic beam deflectingstructure 1210 and the second electromagnetic beam deflecting structure1220 in a fixed relationship to each other. In an embodiment, thepositioning structure is configured to maintain the firstelectromagnetic beam deflecting structure and the second electromagneticbeam deflecting structure in a fixed relationship to each other suchthat an electromagnetic beam 1230 incident on the first electromagneticbeam deflecting structure exits the second electromagnetic beamdeflecting structure as a steered electromagnetic beam 1238.

In an embodiment, the apparatus 1200 includes an electromagnetic beamsteering structure configured to independently rotate the firstelectromagnetic beam deflecting structure 1210 and the secondelectromagnetic beam deflecting structure 1220 relative to a coaxialaxis 1205 such that an electromagnetic beam incident 1230 on the firstelectromagnetic beam deflecting structure exits the secondelectromagnetic beam deflecting structure as a steered electromagneticbeam 1236. In an embodiment, the electromagnetic beam steering structureis configured to rotate the first electromagnetic beam deflectingstructure around the coaxial axis in range of less than one-hundreddegrees.

In an embodiment, the apparatus 1200 includes a beam controller 1280configured to calculate a rotational position of the firstelectromagnetic beam deflecting structure 1210 about the coaxial axis1205 and a rotational position the second electromagnetic beamdeflecting structure about the coaxial axis pointing the steeredelectromagnetic beam 1230 at a selected target. In an embodiment, theapparatus includes an electromagnetic beam generator 1286 configured totransmit an electromagnetic beam to the first electromagnetic beamdeflecting structure.

Various embodiments or variations of the first electromagnetic beamdeflecting structure 1210 are described herein. In an embodiment, thesecond electromagnetic beam deflecting structure 1220 may include one ormore of the embodiments or variations described for the firstelectromagnetic beam deflecting structure.

FIG. 15 illustrates an example operational flow 1300. After a startoperation, the operational flow includes a first deflection angleselection operation 1310. The first deflection angle selection operationincludes selecting a first linear refraction gradient of at least twofirst electronically selectable tangential refractive index gradients ofa first electromagnetic beam deflecting structure. The firstelectromagnetic beam deflecting structure including a first artificiallystructured effective media having at least two firstelectronically-selectable tangential refractive index gradientsdeflecting an electromagnetic beam at a first deflection angle relativeto a coaxial axis. The first deflection angle is responsive to theselected linear refraction gradient of the at least two firstelectronically selectable tangential refractive index gradients. A firstdeflection angle setting operation 1320 includes implementing theselected first linear refraction gradient. A first deflection operation1330 includes passing an incident electromagnetic beam through the firstelectromagnetic beam deflecting structure and generating a first outputelectromagnetic beam. A second deflection angle selection operation 1340includes selecting a second linear refraction gradient of at least twosecond electronically-selectable tangential refractive index gradientsof a second electromagnetic beam deflecting structure. The secondelectromagnetic beam deflecting structure including a secondartificially structured effective media having at least two secondelectronically-selectable tangential refractive index gradientsdeflecting an electromagnetic beam at a second deflection angle relativeto the coaxial axis. The second deflection angle is responsive to theselected second linear refraction gradient of the at least two secondelectronically selectable tangential refractive index gradients. Asecond deflection angle setting operation 1350 includes implementing theselected second linear refraction gradient. A second deflectingoperation 1360 includes passing the first output electromagnetic beamthrough the second electromagnetic beam deflecting structure andgenerating a steered electromagnetic beam having a direction relative tothe coaxial axis that is a vector sum of the first deflection angle andthe second deflection angle. The operational flow includes an endoperation. In an embodiment, the operational flow 1300 may beimplemented using the electromagnetic beam steering apparatus 1200described in conjunction with FIG. 14.

In an embodiment of the second deflecting operation 1360, the steeredelectromagnetic beam has an azimuth angle θ, and a zenith angle φbetween zero and a finite angle from the coaxial axis. The azimuth angleθ and the zenith angle φ are responsive to the first selected linearrefraction gradient and the second selected linear refraction gradient.

In an embodiment, the operational flow 1300 includes receivinginformation indicative of a position of a target in a three dimensionalspace, and determining the first linear refraction gradient and thesecond linear refraction gradient pointing the steered electromagneticbeam at the target. In an embodiment, the operational flow includesinitiating the electromagnetic beam incident on the firstelectromagnetic beam deflecting structure.

FIG. 16 illustrates an electromagnetic beam steering apparatus 1400 anda reference three-dimensional axis 1402. The electromagnetic beamsteering apparatus includes a first electromagnetic beam deflectingstructure 1410 including a first planar electronically-controllableartificially-structured effective media layer 1412 configured to deflectan electromagnetic beam 1430 at a selected first deflection angle of afirst finite range of deflection angles 1434 from a coaxial axis 1405normal to the first effective media layer. The electromagnetic beamsteering apparatus includes a second electromagnetic beam deflectingstructure 1420 including a second planar electronically-controllableartificially-structured effective media layer 1422 configured to deflectan electromagnetic beam at a selected second deflection angle of asecond finite range of deflection angles 1438 from the coaxial axisnormal to the second effective media layer. The first electromagneticbeam deflecting structure and the second electromagnetic beam deflectingstructure have a fixed spatial relationship to each other with planesdescribed by their respective range of deflection angles in asubstantially orthogonal relationship to each other such that anelectromagnetic beam incident on the first electromagnetic beamdeflecting structure exits the second electromagnetic beam deflectingstructure as a steered electromagnetic beam 1436.

In an embodiment, the steered electromagnetic beam 1436 has an azimuthangle θ and a zenith angle φ responsive to the selected first deflectionangle of the first finite range of deflection angles 1434 and theselected second deflection angle of the second finite range ofdeflection angles 1438. In an embodiment, the steered electromagneticbeam has an azimuth angle θ of greater than 180 degrees. In anembodiment, the steered electromagnetic beam has an azimuth angle θ ofgreater than 270 degrees. In an embodiment, the steered electromagneticbeam 1436 has a zenith angle φ between zero and thirty degrees from thecoaxial axis. In an embodiment, the steered electromagnetic beam 1436has a zenith angle φ between zero and twenty degrees from the coaxialaxis. In an embodiment, the steered electromagnetic beam 1436 has azenith angle φ between zero and ten degrees from the coaxial axis.

In an embodiment, the first electronically-controllableartificially-structured effective media layer 1410 is configured todeflect the electromagnetic beam 1430 at a selected first deflectionangle of a first finite range of deflection angles 1434 between one andfive degrees from the coaxial axis. In an embodiment, the first finiterange of deflection angles includes a range between one and ten degreesfrom the coaxial axis. In an embodiment, the first finite range ofdeflection angles includes a range between one and fifteen degrees fromthe coaxial axis. In an embodiment, the second finite range ofdeflection angles includes a range between one and five degrees from thecoaxial axis.

In an embodiment, the first electronically-controllableartificially-structured effective media layer 1410 includes anelectronically-controllable simple binary amplitude or phase gratingstructure. In an embodiment, the first electronically-controllableartificially-structured effective media layer includes anelectronically-controllable artificially-structured blazed grating. Inan embodiment, the electronically-controllable artificially-structuredeffective media layer includes an electronically-controllablemetamaterial layer having tangential refractive index gradient or apiecewise tangential linear refractive index. In an embodiment, thefirst electronically-controllable artificially-structured effectivemedia layer includes a first electronically-switchable layer ofartificially structured effective media. In an embodiment, the firstelectronically-switchable layer of artificially structured effectivemedia includes a first electronically-switchable layer of artificiallystructured effective media having a first electronically-controllabletangential refractive index gradient responsive to a first electroniccontrol signal and deflecting the incident electromagnetic beam 1430 ata selectable first deflection angle of the first finite range ofdeflection angles. In an embodiment, the first electronically-switchablelayer of artificially structured effective media includes a tangentialrefractive index gradient deflecting an incident electromagnetic beam ata first selected deflection angle responsive at least in part to apolarization of the incident polarized electromagnetic beam.

In an embodiment, the second electronically-controllableartificially-structured effective media layer 1420 includes a secondelectronically switchable layer of artificially structured effectivemedia. In an embodiment, the second electronically switchable layer ofartificially structured effective media includes a secondelectronically-switchable layer of artificially structured effectivemedia having a second electronically-controllable tangential refractiveindex gradient responsive to a second electronic control signal anddeflecting the incident electromagnetic beam at a selectable seconddeflection angle of the second finite range of deflection angles 1438.

In an embodiment, the apparatus 1400 includes a positioning structure1455 configured to maintain the first electromagnetic beam deflectingstructure 1410 and the second electromagnetic beam deflecting structure1420 in the fixed spatial relationship to each other. In an embodiment,the apparatus includes a beam controller 1480 configured to select afirst deflection angle of the first finite range of deflection angles1434 from the coaxial axis and to select a second deflection angle of asecond finite range of deflection angles 1438 from the coaxial axispointing the steered electromagnetic beam 1430 at the selected target295. In an embodiment, the beam controller is further configured toinitiate the selected first deflection angle of a first finite range ofdeflection angles and the selected second deflection angle of a secondfinite range of deflection angles. In an embodiment, the apparatusincludes an electromagnetic beam generator 1486 configured to transmitthe incident electromagnetic beam 1430. In an embodiment, thepositioning structure is configured to maintain a spatial relationshipbetween the first electromagnetic beam deflecting structure, the secondelectromagnetic beam deflecting structure, and the electromagnetic beamgenerator. In an embodiment, the first electromagnetic beam deflectingstructure 1410 or the second electromagnetic beam deflecting structure1420 have a thickness 1416 and 1426 respectively that is less than thefree-space wavelength of the incident electromagnetic beam 1430.

Various embodiments or variations of the first electromagnetic beamdeflecting structure 1410 are described herein. In an embodiment, thesecond electromagnetic beam deflecting structure 1420 may include one ormore of the embodiments or variations described for the firstelectromagnetic beam deflecting structure.

FIG. 17 illustrates an example operational flow 1500. After a startoperation, the operational flow includes a first deflection angleselection operation 1510. The first angle selection operation includesselecting a first deflection angle of a first finite range of deflectionangles relative to a coaxial axis. A first configuration operation 1520includes electronically controlling a first electronically-controllableartificially-structured effective media layer of a first electromagneticbeam deflecting structure to deflect an incident electromagnetic beam atthe selected first deflection angle. A first deflection operation 1530includes passing an incident electromagnetic beam through the firstelectromagnetic beam deflecting structure and generating a first outputelectromagnetic beam 1432. A second angle selection operation 1540includes selecting a second deflection angle of a second finite range ofdeflection angles relative to the coaxial axis. A second configurationoperation 1550 includes electronically controlling a secondelectronically-controllable artificially-structured effective medialayer of a second electromagnetic beam deflecting structure to deflectthe first output electromagnetic beam at the selected second deflectionangle. A second deflection operation 1560 includes passing the firstoutput electromagnetic beam through the second electromagnetic beamdeflecting structure and generating a steered electromagnetic beam 1436having a direction relative to the coaxial axis that is a vector sum ofthe first selected deflection angle and the second selected deflectionangle. In an embodiment, the steered electromagnetic beam has an azimuthangle θ and a zenith angle φ between zero and finite angle from thecoaxial axis. The azimuth angle θ and the zenith angle φ are responsiveto the selected first deflection angle and the selected seconddeflection angle. In an embodiment, the operational flow may beimplemented using the electromagnetic beam steering apparatus 1400described in conjunction with FIG. 16. The operational flow includes anend operation.

In an embodiment, the operational flow 1400 includes receivinginformation indicative of a position of a target in a three dimensionalspace, and selecting the first deflection angle and the seconddeflection angle pointing the steered electromagnetic beam at thetarget. In an embodiment, the operational flow includes initiating theelectromagnetic beam incident on the first electromagnetic beamdeflecting structure.

In an embodiment, an electromagnetic beam steering apparatus includes aplanar antenna including a layer of artificially structured effectivemedia having an electronically controlled tangential refractive indexgradient responsive to an electronic control signal and configured todeflect a received electromagnetic beam by a selectable deflectionangle. The apparatus includes a structure configured to mechanicallyrotate the planar antenna about a coaxial axis orthogonal to a majorsurface (x, y) of the planar component in response to a control signal.In an embodiment, the structure is configured to mechanically rotatethrough at least 90 degrees the planar antenna about a coaxial axis. Inan embodiment, the electromagnetic beam is fed into an edge portion ofthe planar antenna.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof.

All references cited herein are hereby incorporated by reference intheir entirety or to the extent their subject matter is not otherwiseinconsistent herewith.

In some embodiments, “configured” includes at least one of designed, setup, shaped, implemented, constructed, or adapted for at least one of aparticular purpose, application, or function.

It will be understood that, in general, terms used herein, andespecially in the appended claims, are generally intended as “open”terms. For example, the term “including” should be interpreted as“including but not limited to.” For example, the term “having” should beinterpreted as “having at least.” For example, the term “has” should beinterpreted as “having at least.” For example, the term “includes”should be interpreted as “includes but is not limited to,” etc. It willbe further understood that if a specific number of an introduced claimrecitation is intended, such an intent will be explicitly recited in theclaim, and in the absence of such recitation no such intent is present.For example, as an aid to understanding, the following appended claimsmay contain usage of introductory phrases such as “at least one” or “oneor more” to introduce claim recitations. However, the use of suchphrases should not be construed to imply that the introduction of aclaim recitation by the indefinite articles “a” or “an” limits anyparticular claim containing such introduced claim recitation toinventions containing only one such recitation, even when the same claimincludes the introductory phrases “one or more” or “at least one” andindefinite articles such as “a” or “an” (e.g., “a receiver” shouldtypically be interpreted to mean “at least one receiver”); the sameholds true for the use of definite articles used to introduce claimrecitations. In addition, even if a specific number of an introducedclaim recitation is explicitly recited, it will be recognized that suchrecitation should typically be interpreted to mean at least the recitednumber (e.g., the bare recitation of “at least two chambers,” or “aplurality of chambers,” without other modifiers, typically means atleast two chambers).

In those instances where a phrase such as “at least one of A, B, and C,”“at least one of A, B, or C,” or “an item selected from the groupconsisting of A, B, and C,” is used, in general such a construction isintended to be disjunctive (e.g., any of these phrases would include butnot be limited to systems that have A alone, B alone, C alone, A and Btogether, A and C together, B and C together, or A, B, and C together,and may further include more than one of A, B, or C, such as A₁, A₂, andC together, A, B₁, B₂, C₁, and C₂ together, or B₁ and B₂ together). Itwill be further understood that virtually any disjunctive word or phrasepresenting two or more alternative terms, whether in the description,claims, or drawings, should be understood to contemplate thepossibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

The herein described aspects depict different components containedwithin, or connected with, different other components. It is to beunderstood that such depicted architectures are merely examples, andthat in fact many other architectures can be implemented which achievethe same functionality. In a conceptual sense, any arrangement ofcomponents to achieve the same functionality is effectively “associated”such that the desired functionality is achieved. Hence, any twocomponents herein combined to achieve a particular functionality can beseen as “associated with” each other such that the desired functionalityis achieved, irrespective of architectures or intermedial components.Likewise, any two components so associated can also be viewed as being“operably connected,” or “operably coupled,” to each other to achievethe desired functionality. Any two components capable of being soassociated can also be viewed as being “operably couplable” to eachother to achieve the desired functionality. Specific examples ofoperably couplable include but are not limited to physically mateable orphysically interacting components or wirelessly interactable orwirelessly interacting components.

With respect to the appended claims the recited operations therein maygenerally be performed in any order. Also, although various operationalflows are presented in a sequence(s), it should be understood that thevarious operations may be performed in other orders than those which areillustrated, or may be performed concurrently. Examples of suchalternate orderings may include overlapping, interleaved, interrupted,reordered, incremental, preparatory, supplemental, simultaneous,reverse, or other variant orderings, unless context dictates otherwise.Use of “Start,” “End,” “Stop,” or the like blocks in the block diagramsis not intended to indicate a limitation on the beginning or end of anyoperations or functions in the diagram. Such flowcharts or diagrams maybe incorporated into other flowcharts or diagrams where additionalfunctions are performed before or after the functions shown in thediagrams of this application. Furthermore, terms like “responsive to,”“related to,” or other past-tense adjectives are generally not intendedto exclude such variants, unless context dictates otherwise.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to one skilled in the art. Thevarious aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

What is claimed is:
 1. An electromagnetic beam steering apparatuscomprising: a first blazed transmission diffraction grating componenthaving a first volumetric distribution of dielectric constantsconfigured to angularly deflect an electromagnetic beam at a first blazeangle; a second blazed transmission diffraction grating component havinga second volumetric distribution of dielectric constants configured toangularly deflect the electromagnetic beam at a second blaze angle; andan electromagnetic beam steering structure configured to independentlyrotate the first blazed transmission diffraction grating component andthe second blazed transmission diffraction grating component about acoaxial axis such that an electromagnetic beam incident on the firstblazed transmission diffraction grating component exits the secondblazed transmission diffraction grating component as a steeredelectromagnetic beam.
 2. The apparatus of claim 1, wherein the firstvolumetric distribution of dielectric constants is divided into aplurality of sub-wavelength voxels having a maximum dimension of lessthan half of a wavelength of the electromagnetic beam, and each voxel isassigned one of a plurality of dielectric constants to approximate thefirst volumetric distribution of dielectric constants.
 3. The apparatusof claim 1, wherein the first volumetric distribution of dielectricconstants is approximated using one or more discrete materials havingspecific dielectric constants.
 4. The apparatus of claim 1, wherein thesecond volumetric distribution of dielectric constants is divided into aplurality of sub-wavelength voxels having a maximum dimension of lessthan half of a wavelength of the electromagnetic beam, and each voxel isassigned one of a plurality of dielectric constants to approximate thesecond volumetric distribution of dielectric constants.
 5. The apparatusof claim 1, wherein the second volumetric distribution of dielectricconstants is approximated using one or more discrete materials havingspecific dielectric constants.
 6. The apparatus of claim 1, wherein thefirst blazed transmission diffraction grating component and the secondblazed transmission diffraction grating component have substantiallysimilar volumetric distribution of dielectric constants.
 7. Theapparatus of claim 1, wherein the first blazed transmission diffractiongrating component and the second blazed transmission diffraction gratingcomponent have dissimilar volumetric distributions of dielectricconstants.
 8. The apparatus of claim 1, wherein the first volumetricdistribution of dielectric constants is selected based on an equationfor a holographic solution.
 9. The apparatus of claim 1, wherein thefirst volumetric distribution of dielectric constants is selected usingan optimization algorithm in which the dielectric constants are treatedas optimizable variables.
 10. The apparatus of claim 9, wherein the realand imaginary parts of the dielectric constants are treated asindividually optimizable variables.
 11. The apparatus of claim 9,wherein the optimization algorithm includes modifying at least oneoptimizable variable and determining a cost function for themodification.
 12. The apparatus of claim 9, wherein the optimizationalgorithm includes determining a gradient of the cost function based onits partial derivatives with respect to each optimizable variable. 13.The apparatus of claim 9, wherein the optimization algorithm includesdetermining a sensitivity vector of a given configuration using anadjoint sensitivity algorithm.
 14. The apparatus of claim 9, wherein theoptimization algorithm comprises a constrained optimization algorithm inwhich the dielectric constants are treated as optimization variablesconstrained to have real parts greater than or equal to approximatelyone and imaginary parts equal to or approximately zero.
 15. Theapparatus of claim 9, wherein the optimization algorithm includesstarting with an initial guess corresponding to a holographic solution.16. The apparatus of claim 1, wherein the electromagnetic beam steeringstructure includes an electronically controlled electromagnetic beamsteering structure.
 17. The apparatus of claim 1, wherein theelectromagnetic beam steering structure is configured to independentlyrotate or counter rotate the first blazed transmission diffractiongrating component and the second blazed transmission diffraction gratingcomponent relative to the coaxial axis.
 18. The apparatus of claim 1,wherein the electromagnetic beam steering structure is configured torotate the first blazed transmission diffraction grating component andthe second blazed transmission diffraction grating component about thecoaxial axis while maintaining an electromagnetic beam path through thefirst blazed transmission diffraction grating component and the secondblazed transmission diffraction grating component.
 19. The apparatus ofclaim 1, further comprising: a beam controller configured to calculate arotational position of the first blazed transmission diffraction gratingcomponent about the coaxial axis and a rotational position of the secondblazed transmission diffraction grating component about the coaxial axispointing the steered electromagnetic beam at a selected target.
 20. Theapparatus of claim 1, further comprising: an electromagnetic beamgenerator configured to transmit the electromagnetic beam.
 21. A methodcomprising: passing an electromagnetic beam through a first blazedtransmission diffraction grating component having a first volumetricdistribution of dielectric constants configured to angularly deflect theelectromagnetic beam at a first blaze angle relative to a coaxial axisand generating a first output electromagnetic beam; and passing thefirst output electromagnetic beam through a second blazed transmissiondiffraction grating component having a second volumetric distribution ofdielectric constants configured to angularly deflect the first outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis and generating a steered electromagnetic beam; the steeredelectromagnetic beam having a direction relative to the coaxial axisthat is a vector sum of the first blaze angle and the second blazeangle.
 22. The method of claim 21, wherein the first volumetricdistribution of dielectric constants divided into a plurality ofsub-wavelength voxels having a maximum dimension of less than half ofthe wavelength of the electromagnetic beam, and each voxel assigned oneof a plurality of dielectric constants to approximate the firstvolumetric distribution of dielectric constants.
 23. The method of claim21, wherein the second volumetric distribution of dielectric constantsdivided into a plurality of sub-wavelength voxels having a maximumdimension of less than half of a wavelength of the electromagnetic beamfrequency, and each voxel assigned one of a plurality of dielectricconstants to approximate the second volumetric distribution ofdielectric constants.
 24. The method of claim 21, further comprising:rotating the first blazed transmission diffraction grating componentaround the coaxial axis to a first selected position; and rotating thesecond blazed transmission diffraction grating component around thecoaxial axis to a second selected position; wherein the steeredelectromagnetic beam has an azimuth angle θ and a zenith angle φ betweenzero and a finite angle from the coaxial axis, the azimuth angle θ andthe zenith angle φ responsive to the first blaze angle, the second blazeangle, the first selected position, and the second selected position.25. The method of claim 24, further comprising: receiving informationindicative of a position of a target; and determining the first selectedposition and the second selected position pointing the steeredelectromagnetic beam at the target.
 26. The method of claim 21, furthercomprising: initiating the electromagnetic beam incident on the firstblazed transmission diffraction grating component.
 27. A methodcomprising: passing a first incident electromagnetic beam having a firstfrequency or a second incident electromagnetic beam having a secondfrequency through a first dual-channel blazed transmission diffractiongrating component having a first volumetric distribution of dielectricconstants deflecting the first incident electromagnetic beam or thesecond incident electromagnetic beam at a first blaze angle relative toa coaxial axis, and generating a first output electromagnetic beamhaving the first frequency or a second output electromagnetic beamhaving the second frequency; and passing the first outputelectromagnetic beam or the second output electromagnetic beam through asecond dual-channel blazed transmission diffraction grating componenthaving a second volumetric distribution of dielectric constantsdeflecting the first output electromagnetic beam or the second outputelectromagnetic beam at a second blaze angle relative to the coaxialaxis, and generating a first steered electromagnetic beam having thefirst frequency or a second steered electromagnetic beam having thesecond frequency; the first steered electromagnetic beam and the secondsteered electromagnetic beam both having a direction relative to thecoaxial axis that is a vector sum of the first blaze angle and thesecond blaze angle.
 28. The method of claim 27, wherein the firstvolumetric distribution of dielectric constants are divided into a firstplurality of sub-wavelength voxels having a maximum dimension less thanhalf of a wavelength of the first frequency or the second frequency, andeach voxel is assigned one of a plurality of dielectric constants toapproximate the first volumetric distribution of dielectric constants.29. The method of claim 27, wherein the second volumetric distributionof dielectric constants are divided into a second plurality ofsub-wavelength voxels having a maximum dimension less than half of awavelength of the first frequency or the second frequency, and eachvoxel is assigned one of a plurality of dielectric constants toapproximate the second volumetric distribution of dielectric constants.30. The method of claim 27, wherein the passing a first electromagneticbeam includes passing a first electromagnetic beam having a firstfrequency and a second electromagnetic beam having a second frequencythrough a first dual-channel blazed transmission diffraction gratingcomponent having a first volumetric distribution of dielectricconstants.
 31. The method of claim 27, wherein the passing the firstoutput electromagnetic beam includes passing the first outputelectromagnetic beam and the second output electromagnetic beam througha second dual-channel blazed transmission diffraction grating component.32. The method of claim 27, further comprising: rotating the firstdual-channel blazed transmission diffraction grating component aroundthe coaxial axis to a first selected position; and rotating the seconddual-channel blazed transmission diffraction grating component aroundthe coaxial axis to a second selected position; wherein the firststeered electromagnetic beam and the second steered electromagnetic beameach have an azimuth angle θ and a zenith angle φ between zero and afinite angle from the coaxial axis, where the azimuth angle θ and thezenith angle φ are responsive to the first blaze angle, the second blazeangle, the first selected position, and the second selected position.33. The method of claim 32, further comprising: receiving informationindicative of a position of a target in a three dimensional space; anddetermining the first selected position and the second selected positionpointing the steered electromagnetic beam at the target.
 34. The methodof claim 27, further comprising: initiating the first electromagneticbeam or the second electromagnetic beam incident on the firstdual-channel blazed transmission diffraction grating component.